Delft University of Technology

Faculty of Applied Sciences

Department of Radiation, Radionuclides and Reactors

Analysis of Two-Phase Flow

Instabilities in Multi-Channel

Natural Circulation Systems

Coen Degen

Supervisor: Martin Rohde

Delft, February 2009

Abstract

It is well known that natural circulation Boiling Water Reactors are subject tosystem-wide density wave instabilities. During the startup of such a reactor,at low pressure and low power conditions, ashing and geysering-induced insta-bilities may occur due to the strong dependence of the saturation temperatureon the local pressure. Previous research showed that these instabilities dependon the applied power, the inlet temperature, the friction distribution and thenumber of parallel channels.

In order to further study the inuence of the number of parallel channels, thecurrent experimental setup CIRCUS at Delft University of Technology is ex-tended to four parallel channels. Comparison with experimental results fromthe previous single channel and double channel setups, is subsequently used todraw conclusions about channel division. For four parallel channels, six dif-ferent stability regimes are encountered. It was found that the instabilities ineach regime could be explained using three phenomena: ashing, geysering andreverse ow. A clear distinction is shown to exist between in-phase oscillations,which are caused by ashing, geysering and reverse ow phenomena and out-of-phase oscillations, which are exclusively associated with geysering and reverseow.

Since the ESBWR design will contain many parallel channels, predictions aremade for the stability behavior in a setup with n parallel channels. This isaccomplished by combining the experimental results with simulations for thein-phase and out-of-phase stability boundaries, based on steady state condi-tions. The measured transitions between the stability regimes are found tocorrespond well with the simulations. From this result, a theoretical extrapo-lation to n channels could be created and it can be concluded that dividing asingle channel into n parallel channels will increase the stability of systems atthe same operational point in the Npch −Nsub plane.

Additionally, the stability of multi-channel systems at uneven power distributionis experimentally investigated using the CIRCUS setup. It is found that in thesesituations the stability of the system is governed by the channel to which thehighest power is applied. Furthermore, the application of a local inlet frictionto one of the channels is shown to have a stabilizing eect for systems at thesame operational point in the Npch − Nsub plane. As a result, it is expectedthat a combined power and friction skew can be utilized to equalize the heattransferred per unit mass over all channels in multi-channel natural circulationsystems.

To ...

Contents

1 Introduction 3

1.1 The need for sustainable nuclear power . . . . . . . . . . . . . . . 3

1.2 The ESBWR principle . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Stability of natural circulation Boiling Water Reactors . . . . . . 5

1.4 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Sustainability 9

2.1 Energy crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Climate change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Nuclear energy today . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Is nuclear power sustainable? . . . . . . . . . . . . . . . . . . . . 14

2.5 Improvements to sustainability by the ESBWR concept . . . . . 15

3 The CIRCUS experimental facility 19

3.1 CIRCUS congurations . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Circus IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Thermocouple calibration . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Partial ow measurement . . . . . . . . . . . . . . . . . . . . . . 21

3.5 Local friction coecients . . . . . . . . . . . . . . . . . . . . . . . 22

3.6 Void measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.7 Heat loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Phenomenological description 27

4.1 Stability behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 The stability map . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3 Comparison of the stability behavior of the dierent CIRCUSsetups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1

5 Simulation and verication 53

5.1 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.2 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3 Modeling of the out-of-phase and a-periodical stability boundaries 56

5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.5 Extension to n channels . . . . . . . . . . . . . . . . . . . . . . . 61

6 Parameter study 65

6.1 Power skew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.2 Inlet friction distribution . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 Implications for the ESBWR . . . . . . . . . . . . . . . . . . . . 73

7 Conclusion and Recommendations 75

7.1 The CIRCUS IV facility . . . . . . . . . . . . . . . . . . . . . . . 75

7.2 Instability phenomena . . . . . . . . . . . . . . . . . . . . . . . . 75

7.3 Theoretical model and simulation . . . . . . . . . . . . . . . . . . 77

7.4 Power skews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A Technical information 90

B Thermocouple calibration 91

C Determination of uncertainty in Npch 92

D Power skew trends in the dimensionless plane 93

E Equipment specications 94

2

Chapter 1

Introduction

1.1 The need for sustainable nuclear power

The world is running into an energy crisis. We are witnessing a time thatcombines record breaking human development with a record breaking increasein demand for energy. The great challenge of the 21st century will therefore bemaking sure that this energy demand can be met, while at the same time dealingwith climate change and other environmental hazards. Virtually everyone agreesthat fossil fuels will not be the way of the future anymore. Although researchinto promising and viable alternatives is currently at full speed, it will still takesome time before they will contribute signicantly to the energy mix.

In the meantime, fossil fuel prices have become volatile and the amount ofinternational quarrels about the delivery of these fuels seems to increase. Whena part of Europe was cut o from the supply of natural gas due to a recentconict between the Ukraine and Russia over its price, Slovakia decided toreemploy two nuclear reactors that were in fact closed as a condition for enteringthe European Union. Apart from the question if this is a development we shouldwelcome, it exemplies how most European countries would deal with a suddenenergy shortage: they turn to proven technology that is not based on importinglarge amounts of resources from countries that do not range among their bestallies. Since no large scale alternative will be available on short term, nuclearenergy becomes an attractive option. At least part of the recent positive shiftin political attitude towards nuclear power can be attributed to this fact.

In addition to this, we must not forget that nuclear power has had a signicantpresence in Europe over the last decades. Some countries more than others, butalmost 35% of all European electrical power is produced by nuclear ssion eventoday. It is therefore very unlikely that nuclear power will disappear from ourenergy mix in the foreseeable future. But of course there is also general concernabout the safety of these reactors. Several events in the past have raised bothawareness and fear for their application. Although a lot of research into reactorimprovements, innovative reactor designs and safety measures has already beenconducted, new and improved reactor designs are currently in development thatboast even higher standards of safety, while also improving the economics and

3

sustainability of the nuclear cycle. In short: There is a need for new, moresustainable nuclear power.

This thesis focuses on the stability of the thermal hydraulic system in a reactorof the newest generation currently on the market: The Economic SimpliedBoiling Water Reactor (ESBWR). A design by General Electric.

1.2 The ESBWR principle

One of the traditional designs for nuclear reactors is the Boiling Water Reac-tor (BWR). In these types of reactors, ordinary water is used as a coolant toremove the heat produced by ssion processes in the core. The coolant is usu-ally pumped into the core from the bottom and, while rising through the fuelassemblies, slowly starts to boil. At the top of the core, the steam is separatedfrom the liquid coolant and is used to drive one or more turbines that produceelectricity by means of a generator. Afterwards the condensed steam is fedback into the system via the periphery of the vessel, also called the downcomersection. A schematic of a typical BWR vessel is shown in gure 1.1a.

Due to the immense power generated within the BWR vessel, a large densitydierence is created between the coolant in the reactor core and the coolant inthe downcomer. This means that the water in the downward channel is heavierthan the hot water and steam in the core and as a result a gravity driven currentwill start to ow through the reactor. This eect is called natural circulation andit is large enough to drive part of the ow through the core. However, naturalcirculation is not enough to extract all the heat produced during ssion fromthe reactor core. Circulation pumps are necessary to drive the ow of coolantthrough the core at high power levels. In the most recent BWR design currentlyin operation, the ABWR (shown in gure 1.1b), these circulation pumps havebeen placed inside the reactor vessel itself, which is a great increase to safety,but they are still necessary to drive the coolant through the core at high power.

The continuing quest for reactor safety has introduced the need for passivelysafe systems. This means that the safety of the reactor does not depend onactive systems, like pumps, but is governed by natural processes. Making fulladvantage of the natural circulation eect, a new BWR design was made thatachieves this goal: the Economic Simplied BWR (ESBWR), in which the needfor circulation pumps was eliminated. To achieve a higher natural circulationlevel, a taller chimney was installed on top of the core (nearly 28 m), thusincreasing the gravitational pressure head. As a result, all heat can be removedfrom the core by natural circulation during operation of the reactor, which isexpected to be about 4500 MWth. A rendering of the ESBWR reactor vesselcan be found in gure 1.1c.

Unfortunately, the elimination of the pumps also comes at a cost. At certainoperational conditions, especially during the startup of the reactor, thermal hy-draulic instabilities may occur due to the feedback between steam productionin the chimney and the gravitational driving force of the system. These insta-bilities give rise to ow oscillations and are undesirable, since they complicatethe operation of the reactor and may have a negative eect on the lifespan ofthe reactor.

4

(a) (b) 1.1b (c)

Figure 1.1: Schematics of Boiling Water Reactor vessels of dierent generations.A typical BWR vessel (a) and the ABWR (b) and the ESBWR (c) reactorvessels.

1.3 Stability of natural circulation Boiling Water

Reactors

The ESBWR design does not come with an external pressurization system, butmakes use of the vapor created in the core to increase the pressure in the systemto approximately 70 bar for nominal operation. Therefore, at the startup of thereactor, this vapor has to be produced rst by operating the reactor at lowpower and (still) low pressure conditions.

This has important implications on the physical properties of the coolant. Dur-ing nominal, high-pressure operation of the ESBWR, the saturation temperatureis practically constant in the chimney section of the facility. At low pressure,however, the saturation temperature is one of the uid properties that becomehighly dependent on the pressure level, as can be seen in gure 1.2a. In addi-tion, the moment vapor is produced in the system, it will immediately take upa large volume in the chimney, caused by the extremely sharp increase of thevoid fraction with the ow quality under low pressure conditions, as can be seenin gure 1.2b. As a result of the decreased density in the core, the driving headis signicantly enhanced, causing the ow through the system to increase tem-porarily. Due to the higher ow level, the core is ooded with relatively coldercoolant from the downcomer, expelling the vapor and consequently decreasingthe density dierence again. The resulting oscillations in the ow through thesystem are commonly referred to as gravity driven density wave oscillations.

Vapor can be produced in the core in dierent ways. In gure 1.3, this isshown schematically in a static situation at dierent pressure conditions. Inthe rst gure (a), the reactor is operating a nominal pressure. The saturationtemperature, Tsat, does not vary signicantly over the height of the system.The coolant is heated in the core until it reaches the saturation temperatureand vapor is produced. In the low pressure situations of gures 1.3 (b) and (c),however, we see that the saturation temperature varies over the height of the

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Figure 1.2: The saturation temperature as a function of the pressure (a) andthe void fraction as a function of the ow quality for dierent system pressures(b).

system due to the decrease in hydrostatic pressure.

At high power and low pressure, the coolant is heated to the saturation tem-perature in the core. Vapor is consequently produced in the core. The resultingdensity wave oscillations caused by this eect, will be called geysering through-out the rest of this thesis, as in dynamical conditions they are similar to the wellknown vapor explosions and subsequent ow reversal. However, during startupof the ESBWR, the power is usually also relatively low, due to the fact thatheat transfer to the bulk of the coolant is relatively low as a result of the exten-sive vapor production. This means that another interesting, but unwanted owoscillation eect can occur. In gure 1.3 (c) we see that due to the low power,the coolant cannot be heated to the saturation temperature in the core. Never-theless, the steam production will continue in the unheated chimney section dueto the fact that the saturation temperature decreases near the top of the core.At a certain height in the chimney, the temperature of the heated coolant willbe equal to the local saturation temperature and vapor will be produced. Thiseect is referred to as 'void ashing' (or just 'ashing'). In dynamic conditions,this eect causes a oscillations in the mass ow, as explained above.

1.4 Objective

Flashing-induced instabilities have been studied both experimentally and nu-merically since their existence was rst pointed out in the 1950s [2]. The eecthas been recreated in several experimental facilities and during an experimentalcampaign in the Dutch natural circulation BWR Dodewaard [3].

At the department of Physics of Nuclear Reactors at Delft University of Tech-nology, recent experimental and numerical investigations of ashing-inducedinstabilities have been conducted by Van Bragt [1], Manera [4] and Marcel[5]. Since, evidently, an actual ESBWR-sized experimental facility would be

6

Figure 1.3: Temperature proles in the reactor vessel at dient conditions. Thedashed line indicated the saturation temperature as a function of height.

very costly and impractical, the scaled facility CIRCUS (CIRCUlation duringStartup) was constructed at Delft University of Technology to investigate thestability behavior of the ESBWR at low pressure conditions. It was found thatat low pressure and low power conditions, ashing is indeed the main causeof instabilities. It was also shown that an unstable operational region existsbetween stable single-phase and two-phase operation.

Although much research into the stability of the ESBWR has been conducted,this thesis is concerned with some of the last remaining questions related to itsstability at low pressure conditions. It was recommended by Manera [4] thatresearch be conducted into the stability eects of a partitioned chimney. If wetake another look at the ESBWR vessel in gure 1.1c, it can be noticed that thechimney section above the core is divided into many separate channels. Thesechannels are installed to guide the two-phase ow in the reactor upwards andto avoid cross ow between neighbouring fuel assemblies, making the behaviorin the reactor more predictable and therefore more controllable. Little is knownabout the stability eects of such a division in a natural circulation system.Some previous experimental work on this subject was conducted by Marcel [5],after tting the CIRCUS facility with a double channel. Due to the coupling ofthe channels at the top and the bottom of the facility, several new instabilitystates were found to be introduced. It remained unclear, however, how thisdivision inuenced the stability of the reactor as a whole.

The main aim of this thesis is therefore to investigate the eect of dividing thesystem into many dierent channels. This investigation can be divided into fourkey parts:

7

1. The phenomenology of the four-parallel channel system is studied in detailby analyzing ow characteristics, temperature proles and vapor produc-tion in the system. This will allow description of the dierent instabilityregimes in the system and provides insight into the driving phenomenaassociated with the instabilities. The resulting experimental data will becompared to experiments obtained with the previous single-channel andtwo parallel-channel setups to make predictions about the behavior of nparallel channel systems.

2. The observed dierences between the stability phenomena are used toformulate boundary conditions for a simple steady state model describingthe stability boundaries of the parallel channel system. This model will betested against the available experimental data from the dierent CIRCUSsetups.

3. Consequently, this model is extrapolated to a system with n parallel chan-nels to predict the occurrence of stability regimes in systems that aredivided into a larger number of parallel channels.

4. A last objective that was set, is to investigate the eect of a power skewbetween parallel channels. For this purpose, experiments are conductedin the four parallel channel system, in which the power is varied betweenchannels. Additionally, investigations are conducted into the eect onstability of a proposed method to compensate for a power skew by applyingdierent localized frictional pressure drops over the channels.

1.5 Outline of this thesis

There is hardly any engineering project to be found that can aord not to beconcerned about its societal context. Delft University of Technology has decidedto emphasize this context by incorporating it into the programme by means ofspecialized courses on ethics and sustainability. This project was conducted inthe framework of the special track Sustainability in Technology and in this light,its place in the societal context is rst described in chapter 2.

After that, the CIRCUS facility is briey described for reference in chapter3, before continuing to the detailed description and explanation of the diverseinstability states found to occur in the system in chapter 4. In this chapter,a connection will also be made with the ndings of Manera and Marcel atrespectively the single channel- and double channel setup.

In the subsequent chapter 5, a simple steady state model, based on the observa-tions in chapter 4 will be presented. The model is compared to the experimentalresults by Manera and Marcel and is then extended to a system which is dividedinto many channels.

Chapter 6 will deal with investigations into the stability behavior of the systemunder a power skew and the application of localized friction at the bottom of thechannels. The implications of the results to the ESBWR will also be discussedin this chapter.

8

Chapter 2

Sustainability

The issue of sustainability is often a many-sided one. This is denitely the casein relation to nuclear power generation, due to strong (and diering) sentimentsthat people have regarding its application. Nevertheless, in recent years, thegeneral public seems to have renewed its interest in nuclear power. It is hardto guess if this change in attitude is due to the fact that technology as a wholebecomes an ever larger and more accepted part of our daily lives, or perhapsdue to the simple fact that nuclear power for once nds itself on the popularside of a waste issue: the discussion about climate change.

This chapter will not be a complete overview of the sustainability of nuclearpower. The subject is simply too broad and sometimes too complicated toprovide a full account of all the details. Though most of them are interestingand many-sided, this thesis is not the place to discuss them all extensively.Instead, the chapter will focus on the position of nuclear power in the light ofmodern trends, in particular two themes specically related to the improvementsby the ESBWR: safety and economy.

2.1 Energy crisis

There hardly has been a time in which the discussion about energy has beenas global as today. Although worries about peak oil largely seem to have beenreplaced by outcries on the reduction of CO2 emissions, the fact remains thatthe fossil fuel supply is limited. Often even more so in availability, as recentsurges in oil prices and conicts about the delivery of natural gas have shown.Important pockets of fossil fuel reserves are concentrated in only a few countries,that consequently have a large inuence on their distribution.

Moreover, in the last decades, we are experiencing unprecedented levels of hu-man development. The incorporation of technology in virtually any part ofdaily life in the western world and the rapid development of, for example, sev-eral Asian countries, have increased the demand for energy even more: Trendsthat are not expected to weaken over the next decades. In addition, the world'spopulation is still growing rapidly, as can be seen in gure 2.1a, contributing toan estimated 50% rise in energy demand until 2030 [7, 10].

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Figure 2.1: The historic and projected development of the world's population(a) and the total and projected world total energy consumption (b). Sources:UN department of economic and social aairs [9], EIA [10].

Despite remarkable progress in renewable methods of energy supply, e.g. solar,wind and biomass, a secure power supply based on their application is notexpected on the short-term. Even the most optimistic scenarios predict nomore than a 15% share of these renewables in 2030 [8] Extending the currentexponential growth to the year 2050, still only means a renewable share of 45%in the energy mix. It is questionable, however, if the current growth can besustained at the same pace for all renewables. At the same time, as we will seein the next section, ambitious goals have been set for the reduction of greenhousegases to the environment. Making sure that there will be enough energy in thelong run, without drastically inuencing our environment, will therefore be oneof the major challenges of the century.

2.2 Climate change

In addition to the rising energy demand, research has shown that it is extremelylikely that the warming of the planet is induced by human activity [11]. Throughthe emission of greenhouse gases, of which especially carbon dioxide plays a sig-nicant role, human development is inuencing the world's climate. Realizationof the extent of the problem has urged governments worldwide to take measuresto mitigate the rate of increase of CO2 in the atmosphere. It is, however, safeto say that limiting these emissions is easier said than done under the trendsdescribed in the last section.

The Carbon Mitigation Initiative from the Princeton Environmental Institute[12] has an insightful way of demonstrating the seriousness of the problem.In gure 2.2a, the historical CO2 emissions have been plotted. In the samegure, predictions of future emission levels are displayed, based on a "businessas usual" scenario. To be able to halt the increase of CO2 emissions in thefuture, measures should be taken that amount to a total reduction of 8 billionTons of CO2 yearly in 2055. If we divide this amount (the stabilization triangle

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in gure 2.2a) into eight equal 'wedges,' we can suggest eight measures thatwould save up to 1 GTon of emissions in 2055. This is depicted schematicallyin gure 2.2b.

In the list below, several measures proposed by the CMI [12] that would amountto such a reduction have been summed up.

Double the fuel eciency of the world's cars or halve the total distancetraveled by car in the world. There are about 600 million cars in the worldtoday, with 2 billion predicted for 2055.

Produce today's electricity with double the eciency. Average coal planteciency is around 32% nowadays.

Use today's best eciency practices in all residential and commercialbuildings.

Build 1000 of today's Carbon storage facilities. There are currently threestorage projects that each inject 1 million tons of CO2 into the groundper year.

Install 1 million 2 MW windmills to replace coal based electricity. Thismeans increasing the currently installed wind electricity capacity by afactor thirty.

Install 20.000 square kilometers of solar electricity. This would mean in-creasing current capacity 700 times.

Eliminate tropical deforestation or plant new forests over an area the sizeof the continental US.

Triple the world's nuclear electricity capacity by 2055. The CO2 emissionsin the fuel- and lifecycle of a nuclear power plant are negligible comparedto many other means of electricity generation, as can be seen in gure 2.3.

For most of the above measures, it is very questionable if they can be achievedbefore 2055. Moreover, we would need to achieve all of the examples above(or equivalent measures) to only stabilize the total emission of CO2 in thefuture. To reduce these levels, we would even have to go through much greaterlengths. From this analysis we can conclude that if we are to realistically reduceCO2 emissions, we must work on it in all possible elds. Due to its low CO2

emissions and proven availability, nuclear power generation therefore becomesan attractive option and is likely to be part of any solution.

2.3 Nuclear energy today

The use of nuclear energy for commercial power generation has been a topicof vivid discussion in many countries. There have been large dierences ingovernmental policies over the last decades. France, for example, presentlyderives more than 75% of its electricity from nuclear energy, while the Germangovernment (at 25% currently also a major user of nuclear power) has recently

11

(a)

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Figure 2.2: The historical and future CO2 emissions as predicted by the CarbonMitigation Initiative (a) and a magnication of the stabilization triangle (b).Source CMI[12].

12

Figure 2.3: CO2 emissions from traditional means of energy supply. Source:IAEA [13].

Figure 2.4: The share of nuclear power in produced electrical energy worldwide(percentage). Source: IEA [10]

committed to gradually phasing out the use of nuclear energy over the comingdecades [14].

Nevertheless, the share of nuclear power in electricity production worldwide hasnot changed much since the end of the 1980s. As becomes clear from gure 2.4,the proportion of nuclear power in the electricity mix has stabilized at around16%. In Europe, this number is around 35%, mainly due to heavy relianceon nuclear power in France. At the moment, 436 nuclear power reactors are incommission and 43 new reactors are under construction, partly as a replacementfor reactors that will shortly be decommissioned [14]. Most notably, eleven newconstruction sites are found in China, which additionally has concrete plans foranother 26 reactors in the near future.

As a result, we can conclude that although nuclear power has not been 'infashion' over the last decades, nuclear power still supplies a signicant part ofelectricity worldwide. A part that we cannot just replace by other means ofelectricity generation, in the light of the aforementioned developments.

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2.4 Is nuclear power sustainable?

After considering the information in the previous sections, a rst concludingremark we can reasonably make is that it is unlikely that nuclear ssion as ameans of electricity production will disappear in the near future, regardless of itsaptitude as a long term sustainable solution, simply because we have no way ofcompensating its contribution to the energy mix. This is, however, completelyunrelated to the question if nuclear power should disappear. Due to the fact thatnuclear technology is a mature technology with a low CO2 impact and is alsostill developing rapidly, it seems far more likely that nuclear power generationwill be part of any energy solution for the foreseeable future. For this reason, itis expected by the International Energy Agency that the share of nuclear powergeneration will rise over the next decades [7].

We may have concluded that nuclear power is unlikely to disappear, but thatdoes not yet answer the question of sustainability. To be sustainable, it should- to quote the most widely used denition of sustainability - "meet the needs ofthe present, without compromising the ability of future generations to meet theirown needs." This is usually called the Brundtland denition of sustainability. Itcan be divided into three separate topics: environmental, economic and socialsustainability.

So what does this denition imply for nuclear power? Is it sustainable? In thestrict sense of this denition, the answer is probably no. Although there havebeen many signicant improvements recently and a lot more can be expectedin the near future, problems of dealing with the waste and proliferation issuesare still present for example. But then again, according to the same denition,practically none of our current power generation methods is sustainable either,including the ones called renewables. An example we have already encounteredin gure2.3, is solar photovoltaic conversion of energy, which still produces arelatively large amount of CO2 over its complete lifecycle. Other examplesare the current use of biomass, which cannot possibly be called socially norenvironmentally sustainable due to its competition with food production andextensive deforestation to make room for plantations, and the application ofhydro power, which is often questionable from a sustainable point of view asa result of large scale ooding of natural areas and the associated risk of damfailure to people living downstream.

Eventually, many methods have the potential to become sustainable methodsof power generation, but perhaps so does nuclear power. The reality is that weare still a very long way from the sustainability of anything. Since the chal-lenges described in the last sections are presenting themselves today, the bestthing to do is compare the alternatives and indicate the direction of sustain-ability. To put it more popularly: We cannot simply burn coal until we ndthe ultimate sustainable solution. Returning to gure 2.3, we can rightly saythat as a contribution to the reduction of CO2 emissions, nuclear power is moresustainable than most other means of power generation. In that sense, elimi-nating nuclear power as an option might in fact be a very unsustainable thingto do. In other respects, however, it might be a sensible decision. We will haveto make decisions about the application of the dierent alternatives based onwhich matters are more pressing and in what way we can move as far in the

14

Figure 2.5: A breakdown of the typical buildup of the nuclear electricity gener-ation cost [15].

direction of sustainability as we currently can.

As a result of the discussed trends, we can conclude that there will very probablybe a need for more sustainable nuclear energy in the near future. In the mean-time, we can improve the sustainability of existing nuclear power generation byconducting research and designing new reactor types. The ESBWR design is anexample of the improvement of the social (safety) and economic sustainabilityof Boiling Water Reactors. These themes will therefore be discussed in a littlemore detail in the next sections.

2.5 Improvements to sustainability by the ES-

BWR concept

2.5.1 Economics

Nuclear power plants are very capital intensive. In contrast to most other fuelconsuming means of power production, it is the initial investment that mostlydetermines the eventual price of electricity. In gure 2.5, a breakdown of thetypical cost of nuclear electricity generation is shown. The large amount ofnancing required for building a reactor makes that it has to be slowly amortizedover its lifetime. This means that the characteristic time window involved withthe economics of new commercial nuclear power installations can be as long as60 years in some cases. As a result, construction is only feasible if long-termcompetitive electricity prices can be guaranteed. Every eort to reduce the

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Figure 2.6: The increasing simplicity of the Boiling Water Reactor Design.

initial investment, while maintaining safety, is therefore a welcome improvementin this respect.

In the past, nuclear power generation has shown to produce electricity at acompetitive price, but many of the safety improvements in new facilities, havecome at extensive nancial cost, contributing to an even higher initial invest-ment cost. The great improvement of the ESBWR design is that it decreasesconstruction and operational costs, while at the same time further improvingthe safety of the reactor.

Due to the fact that the ESBWR only uses natural circulation to drive the owthrough the core, the design of the reactor vessel can be more simple than withmore traditional designs (as schematically displayed in gure 2.6. The simplerdesign results in a reduction of initial investment due to lower production costof the vessel and the fact that circulation pumps and the associated piping,control and safety measures can be left out completely. In addition, costlypump maintenance programs are no longer necessary. It is therefore expectedthat these improvements will signicantly increase the economic feasibility ofBWR power generation.

2.5.2 Safety

Much of the research concerned with the development of nuclear reactors hastraditionally focused on safety. Catastrophical events in the past have con-tributed to this strong focus and although these events occurred in facilitiesthat are uncharacteristical for modern western nuclear plants, safety remains- and righly so - a strong emphasis in today's social, political and researchagendas. For sustainable application, referring to the Brundtland denition insection 2.4, it must be made sure that nuclear power will not form any long-termrisks for society and the environment. The associated current 'sustainable direc-tion' would therefore be bringing the safety of reactors within acceptable limits.In addition, the application of nuclear power generation in the energy mix ishighly related to the level of public acceptance, in which safety considerations

16

Reactor design maximum core damage frequency (yearly)

BWR/4 1 · 10−5

BWR/6 1 · 10−6

ABWR 2 · 10−7

ESBWR 3 · 10−8

AP1000 5, 09 · 10−7

EPR 6, 1 · 10−7

Table 2.1: Maximum core damage frequencies for several Boiling Water Reactordesigns and two modern Pressurized Water Reactor designs: The AP1000 andthe European Pressurized Reactors. [6].

are a major driver. One of the most important aspects of the sustainability ofnuclear reactors will therefore be their safety.

Along with many other improvements, the generation of nuclear reactors thathas recently become available on the market, boasts passive safety measures.This means that no active intervention is necessary to guarantee the safety ofthe reactor. The ESBWR also belongs to this new generation. As naturalcirculation drives the ow, removing the heat from the core does not requireoperator action anymore. As a result, cooling of the core is guaranteed underall conditions. The diculties start, however, if we try to quantify the accept-ability to society. One way to do this, is by conducting a risk assessment. Intable 2.1, the calculated maximum core damages frequencies that are part ofthe extensive risk calculations required for the approval of a new reactor type,are displayed. This number is a term used in the risk assessment to indicate thelikelihood of an event that would cause maximum damage to the core and possi-ble discharge of radioactive material to the environment. From the gures in thetable, it becomes clear that the likelihood of a major incident in the ESBWRis signicantly decreased compared to earlier BWR designs like the BWR/4,BWR/6 and ABWR that are presently in operation. Also in comparison tomodern Pressurized Water Reactors, on which construction has begun in Chinaand Finland, the ESBWR boasts signicant improvements in this respect.

Nevertheless, can these risks be deemed acceptable? One thing we can do iscompare the maximum core damage frequency gures to other major eventsthat would result in similar, or worse consequences to society. Dams for hydro-electric power generation, for example, have a calculated average failure rate of10−5 per year [16, 17]. In populated areas this could have severe consequences,as multiple events in the past have already shown [14]. An example that mightbe more apt for Delft, is the estimated failure rate of coastal protection. For theprovince of South-Holland, the probability of severe ooding incidents causingan estimated death toll of thousands, is around 4 · 10−4 yearly [18].

More quantitatively, this comparison can be formulated using the concept ofrisk, which is dened as the probability of an event occurring (P ) times theimpact of that event (I). In the form of an equation:

R = P × I

If we leave the damage to economy out of the comparison, the ood risk can

17

be calculated to amount to 0, 23 casualties per year [18]. It is hard to estimatethe impact of a nuclear incident. But even if we range the impact in thousandsof casualties, which is a highly exaggerated number, the risk will still be threeorders of magnitude smaller.

Of course, many comments can be made in regard to this approach, but thesimple fact remains that the ESBWR design brings the risk associated with theapplication of nuclear power to unimaginably low numbers. In practice we cantherefore conclude that the ESBWR design answers the need for short-term,sustainable nuclear power.

18

Chapter 3

The CIRCUS experimental

facility

3.1 CIRCUS congurations

To simulate the conditions occurring in the ESBWR during startup of the re-actor, there was a need for a scaled facility to conduct experiments with. Forthis purpose, the CIRCUS facility was constructed. The present CIRCUS setupis in fact the third, modied setup. Originally, it was constructed as a singlechannel system, but it was later tted with double and even four parallel chan-nels to facilitate the investigation of the eect of chimney division on reactorstability. For the remainder of the report, these dierent congurations will bereferred to as CIRCUS I, CIRCUS II and CIRCUS IV respectively. The totalcross-sectional surface area of the channels was kept approximately the sameto simulate the division of a single riser into several sections, as can be seen ingure 3.1. The core section was left unchanged in each conguration.

The exact measures for the dierent congurations can be found in table 3.1.Detailed descriptions of the rst two CIRCUS set-ups are provided by Manera[4] and Marcel [5], whereas the CIRCUS IV facility, the implementation of voiddetection and certain aspects of the calibration of the setup will be discussed inthe next sections.

Figure 3.1: The total cross-sectional area of the chimney sections in the dierentCIRCUS congurations, viewed from the top.

19

Circus I Circus II Circus IV

Chimney diameter 47 mm 33 mm 24, 4 mm

Chimney cross-sectional area 1, 73 · 103 mm2 8, 55 · 102 mm2 4, 68 · 102 mm2

Total chimney cross-sectional area 1, 73 · 103 mm2 1, 71 · 103 mm2 (-1%) 1, 87 · 103 mm2 (+8%)

Core inner diameter 20, 4 mm 20, 4 mm 20, 4 mm

Heating rod diameter 12, 5 mm 12, 5 mm 12, 5 mm

Core cross-sectional area 2, 04 · 102 mm2 2, 04 · 102 mm2 2, 04 · 102 mm2

Downcomer diameter 51 mm 51 mm 25, 5 mm

Bypass Channel diameter 10 mm 10 mm 10 mm

Core length 2038 mm 2038 mm 2038 mm

Chimney length 3068 mm 3068 mm 3559 mm

power range per rod 0 - 3 kW 0 - 3 kW 0 - 3 kW

Pressure range 1 - 5 bar 1 - 5 bar 1 - 2 bar

Table 3.1: Relevant characteristics of the dierent CIRCUS congurations.

3.2 Circus IV

The CIRCUS facility in its current conguration is shown schematically in g-ure 3.2. Besides having four parallel channels, there are a few other dierencesbetween CIRCUS IV and its predecessors. The pressure vessel that was presentin the previous setups, has been removed and the steam dome is placed directlyon top of the chimney exit. Also, a pre-heater has been installed near the coreinlet, that can be used, when necessary, to more accurately set the temperatureof the water entering the core. As indicated in table 3.1, CIRCUS IV is some-what taller than its predecessors. This is due to the fact that the top of thechimney section was rebuilt in a slightly dierent conguration to accommodatefor four parallel channels. In addition to this, it was tted with extra valves tobe able to impose an exit friction.

For the rest, the setup has largely remained the same. Each of the four chimneysis installed on top of a separate channel that contains an electrically heated rod.Each rod can be set to deliver a power from 0-3 kW to the surrounding water.Below the core inlet, a set of valves is included, which makes it possible to addfriction to each channel separately or to close o channels completely. Over thispart of the setup, dierential pressure sensors have been installed, capable ofmeasuring both negative and positive pressure drops.

3.3 Thermocouple calibration

At the start of this project, it was made sure that all thermocouples were insertedinto the ow at exactly the same distance, i.e. 5 mm from the inner wall of thechannels. Subsequently, all thermocouples in the setup were calibrated againstthe PT100 at the central inlet below the core. This is done by recording thecooling down of the setup under forced ow conditions. The acquired curves foreach thermocouple and the PT100 are then tted with a second order polynomialcurve in Matlab. The thermocouple signals are then adjusted for their deviation

20

Figure 3.2: A schematic version of the CIRCUS experimental setup.

from the PT100 t.1After correction, all thermocouple signals are found to bewithin a range of approximately 0,5 K. The calibration results can be found inappendix B. In turn, the PT100 at the inlet is calibrated manually by detachingit from the setup and measuring its response signal while keeping it in meltingice and boiling water at known atmospheric pressure.

3.4 Partial ow measurement

For a detailed investigation of the instability phenomena, we are not only inter-ested in the ow through the primary circuit, measured by the ow meter at thebottom of the setup. It will also be useful to determine the partial ows, i.e. theow through each of the four channels separately. Using the dierential pressuresensors at the inlet channels below the core, this partial mass ow through thechannel can be calculated using te following relation:

M2i =

2A2ρ

Kin,i∆pi (3.1)

where ∆pi is the measured pressure drop over each inlet channel, Kin,i the localfriction coecients in the corresponding channels andMi the mass ow througheach channel. Most of this analysis has been done by Weppelman [19].

1This has been done before by Weppelman [19], but at that point the radial positions ofthe thermocouples in the channels were unknown and insulation had not yet been added tothe setup.

21

Kin,i

Inlet channel 1 3, 54± 0, 14Inlet channel 2 3, 42± 0, 12Inlet channel 3 3, 43± 0, 12Inlet channel 4 3, 38± 0, 14

Table 3.2: The friction coecients related to the valves and bends in the inletchannels below the core.

Due to the large measurement range of the dierential pressure sensors and asa result of thermal eects on the arrangement of the pressure sensors, Wep-pelman found that uncertainties in the determination of the pressure drop areapproximately 130 Pa. For certain conditions this is too large to calculate asensible value for the mass ow, for example for single phase natural circulationconditions, with typical pressure drops below 100 Pa. On the other hand, forlarger mass ows, as during ashing or reverse ow phenomena, calculation withsmall relative uncertainty is possible.

3.5 Local friction coecients

Relation (3.1) is also used to determine the friction coecients of certain parts ofthe facility. For example, to facilitate easier comparison to the previous setups,the common inlet friction coecient, Kin, is manually set to a comparable valueby means of adjusting a valve in the downcomer.2 Afterwards, the frictioncoecient is calculated by recording the pressure drop over the relevant part ofthe setup for a range of dierent mass ows and applying equation (3.1). Allfriction coecients have been determined in high (forced) ow conditions. Dueto the comparatively low contribution of the channel wall friction to the pressuredrop in these conditions, the latter has been neglected in the determination ofthe local friction coecients.

In this case, the inlet friction coecient was set to Kin = 8, 9, a value closethe the value used by Marcel [5] (K = 8, 65). This friction was left unchangedduring measurements, unless indicated dierently. In the same way, the frictioncoecients for the inlet valves have been previously calculated by Weppelman[19]. In table 3.2, the values for these frictions can be found. The central exitfriction, which is caused by the recombination of the four channels at the top ofthe chimneys, was found to be Kex = 1, 7.

3.6 Void measurement

For a thorough understanding of the phenomena occurring in the chimney sec-tions, it is of interest to know the (axial) location of void production and col-lapse. In the preceding CIRCUS setups, this was achieved by applying wire-

2The position of the inlet friction valve is indicated in gure 3.2.

22

Figure 3.3: One void sensors attached to the set-up (top view).

mesh sensors, gamma-transmission techniques and conductivity needle probes.3

Unfortunately, each of these methods has its disadvantages and are not appliedto CIRCUS IV due to practical considerations or simply because it became toocostly to implement enough of them for a complete picture about void produc-tion in a setup with four separate chimneys.

Instead, a simple optical sensor was developed and implemented as a part ofthis project. It was shown to produce good results in the detection of voidpassing through the chimneys. A total of 60 of these simple optical void sensorshave been installed at regular intervals on the outside of the glass chimneysections (15 per chimney). The sensors consist of a focused red power-LED anda photodiode, embedded into a teon ring, on opposite sides of the glass channelwall. The technical specications of these sensors can be found in appendix E.In gure 3.3, a single sensor is depicted schematically and in gure 3.4, twophotographs of the sensor array attached to the set-up is displayed. Since aninsulating foam layer will cover the installed sensors during experiments, noisefrom surrounding light sources on the photodiode signal is eliminated.

When a vapor bubble passes the bundle of red light in the channel, it brieydisrupts it due to the refraction of the light at the bubble boundary. This causesa sharp decrease in the photodiode signal. It is clear that a sensor of this typeis only able to indicate the presence of vapor in the chimney rather than thevapor fraction. A typical output signal from the photodiode is shown in gure3.5 (top). The downward uctuations of the signal indicate the presence ofvapor at the location of the sensor. The upward uctuations of the signal inthis case are due to the applied lter during data collection. Directly below thephotodiode data, the temperature in the chimney at approximately the sameaxial location is displayed to provide an idea of the conditions in the chimneyover time.

As indicated in the magnications in gure 3.5, the sensors clearly capture boththe fast signal uctuations associated with bubbly ow (in magnication (a))and the larger void ashing and geysering events (magnication (b)). Althoughthe signals in the magnifactions look quite noisy, the registered peaks can com-pletely be attributed to vapor passing in the chimney. The noise level itself is

3More information about the applied techniques can be found on pp. 7-13 in [4] and onpp. 77 in [5]

23

Figure 3.4: A set of pictures of the array of void sensors attached to the CIRCUSIV set-up.

0 500 1000 1500 2000 25000

0.5

1

Time [s]

Rel

ativ

e ph

otod

iode

sig

nal

500 1000 1500 2000 2500

85

90

95

100

105

Tem

pera

ture

ch

imne

y ou

tlet [

°C]

Time [s]

Magnification (a) Magnification (b)

800 805 810 815 820 825 830 835 8400.5

0.6

0.7

0.8

0.9

1

1.1Magnification (a)

Rel

ativ

e ph

otod

iode

sig

nal

Time [s]2400 2410 2420 2430 2440 2450 2460 2470 2480

0.5

0.6

0.7

0.8

0.9

1

1.1

Time [s]

Rel

ativ

e ph

otod

iode

sig

nal

Magnification (b)

Figure 3.5: Void sensor data (top) and the temperature at the chimney outlet(centre) after starting up the Circus IV facility at full power (11 kW), as well asmagnications of the void sensor signal for the indicated domains (bottom).

24

only 0,5% of the photodiode signal.

The array of LED-Photodiode Sensors is used to determine the axial position ofvoid in the riser sections. The signal received from the photodiodes is registeredby a separate computer system at 1000 Hz per channel. Synchronization of thissystem with the regular data acquisition system in CIRCUS IV (which registersall other observed parameters) is conducted by applying a manual trigger signalto one input channel in each system. A number of Matlab scripts have beenwritten to process the photodiode signals.

To test the agreement of the photodiode signals with the vapor in the chimneysections, high speed camera images were recorded during ashing phenomena.The data recorded by the sensor was shown to correspond very well to theindividual bubbles passing the sensor in the chimney. Although the informationfrom the sensors has, in the course of this Master project, only been used todetermine the location of void production and the direction of the vapor ow, thedetailed detection of individual bubbles and the distinct dierentiation betweenthe two magnied signals provides hope for a possible future determination ofow regimes based on photodiode data. It is expected that bubbly, slug andchurn ow can be individually detected on the basis of characteristic signalsfrom the void sensors.

3.7 Heat loss

To limit heat losses to the surroundings, foam insulation has been wrappedaround the four chimney sections, as was also done with the CIRCUS I and IIchimneys. Nevertheless, there is still some heat loss, although it will be hardto estimate due to the irregular shape of the facility. At a water temperatureinside the facility of approximately 99 °C, the outside of the foam reaches anaverage temperature of 35,9 °C in surroundings of 28 °C.

This means that the heat loss in the chimney is very small compared to the heatloss in the core. The core section is not insulated and the four glass channelscontaining the heating rods are open to the surrounding air. Since the owin the core sections has been turbulent during all measurements conducted inthe CIRCUS IV facility, we will neglect the heat transfer coecient from thewater to the glass wall and assume that the inside of the wall is at the sametemperature as the water.4 We can therefore estimate the heat loss in the coreby applying Fourier's law in cylindrical coordinates to the glass wall:

φ′′ = −λdTdr

(3.2)

4A quick estimation of the heat transfer coecient shows that this assumption is acceptable.If we approximate the glass pipes as a at wall, we can calculate the overall heat transfercoecient as follows:

1

htot=

dbl

< Nu > λH20+dwall

λwall

Where the Nusselt number in the core varies between 20 and 75 for CIRCUS IV operationalconditions (and is even higher during forced ow). Since the thermal boundary layer, dbl, is atmost of the order of the channel width, we see that the rst term becomes much smaller thanthe second. Neglecting the resistance to heat transfer from the water to the glass is thereforeallowed.

25

or

φ = −λA(r)dT

dr= −λ2πrL

dT

dr(3.3)

If we rewrite the equation to isolate the dierential:

dT

dr= − φ

λ2πrL(3.4)

and integrate from the inside of the glass wall R1 to the outside, R2, we get

T1 − T2 =φ

λ2πLln

(R2

R1

)(3.5)

where evidently T1 is the temperature at the inside of the glass tube and T2

at the outside. In a forced ow conditions, with a constant average watertemperature of 95,1 °C, the average outside wall temperature is measured tobe 92,2 degrees, with a wall diameter of 3 mm. Using equation 3.5, we cancalculate that this amounts to a total heat loss of approximately 1500 W overthe four core sections. Radiation heat losses can be neglected in comparison tothis number. We must be aware, however, that assuming these temperatures tobe constant is quite a stretch during regular operation.

26

Chapter 4

Phenomenological description

This chapter will deal with the description of the instability phenomena en-countered in the CIRCUS IV facility. First, the instability phenomena will beclassied on the basis of their phenomenology and organized into a referencemap in the power-subcooling plane, the so called stability map. This map willsubsequently be compared with stability maps created for the CIRCUS I andII setups. From this comparison, we will be able to draw some rst conclusionson the inuence of chimney division on stability.

4.1 Stability behavior

Depending on the conditions in the facility, six dierent kinds of stability behav-ior are encountered in CIRCUS IV. These behaviors have mainly been classiedon the basis of the ow in the primary circuit. For example, if we x the powerapplied to the heating rods in the core and simply have a look at the primaryow through the facility while slowly increasing the inlet temperature, we ob-tain the mass ow characteristics displayed in gure 4.1. In order of appearancefrom left to right (so from high subcooling to low subcooling) we encounter:High subcooling stable ow, in-phase ow oscillations (also called intermittentoscillations), a-periodical oscillations, out-of-phase oscillations, higher order out-of-phase oscillations and low subcooling stable ow. The transition to the lowsubcooling stable ow was not experimentally detected in low inlet friction con-ditions (although the state itself was1) and is therefore estimated in gure 4.1for the sake of completeness.

If we compare the observed regimes with the ones found by Marcel [5] in CIRCUSII, we see that one type of unstable behavior has been added: the higher orderout-of phase oscillations. Although at rst sight this behavior might not seemvery dierent from the regular out-of-phase oscillations, we will see in section4.1.5 that the oscillation is caused by dierent phenomena. We will also see thatmore dierences have been found with respect to the instabilities in CIRCUS

1In section 4.1.6 it is explained how the low subcooling stable ow state can be achievedin the measurable range, while the transition to this state cannot be exactly determined.

27

Figure 4.1: The primary mass ow signal in dierent stability regimes atP = 2200W/rod and Kin = 8, 9. The low subcooling stable ow boundaryis estimated.

t1 t2 t3

Ch. 1 F ↓ FCh. 2 ↓ G ↓Ch. 3 ↓ G ↓Ch. 4 ↓ G ↓

Table 4.1: An example of a timetable used to describe the instabilities occurringin the setup.

II and that the conguration of the regimes in the power-subcooling plane isquite dierent. All stability regimes and their characteristics, are described inthe next paragraphs.

Before continuing to the description of the instabilities themselves, one conclu-sion about them is best explained at this point. All of the observed instabilitybehaviors can be considered to be caused by three main phenomena: Flashing,geysering and reverse ow. Two of these phenomena, ashing and geysering,have been explained in the introduction. The last one, reverse ow, is denedas a ashing- or geysering-induced reverse mass ow in one or more of the chan-nels. Since the description and especially the explanation of the instabilitiesis often not straightforward, time tables will be applied to clarify which of thethree phenomena plays a role at what point in time. An example of such a tableis provided in table 4.1. The rows indicate the dierent channels in the setup,while the columns indicate moments in time that are of interest, but are notnecessarily separated by an equal amount of time. The occurrence of the mainphenomena are indicated by symbols. F for ashing, G for geysering and ↓ forreverse ow. For example, at t1 we see a ashing event in channel 1 and a si-multaneous reverse ow in channels 2-4. This tool will prove to be instructionalwhile analyzing the process behind the dierent instabilities.

4.1.1 High subcooling stable ow

At relatively low inlet temperatures, there is only very little production of vaporin the system. In this case, the system displays no mass ow oscillations due tovoid ashing, as can be clearly seen in gure 4.2a. The small downward peaksin the signal are caused by the ow meter itself and do not represent mass owoscillations. The regime is characterized by identical axial temperature proles

28

(a) (b)

Figure 4.2: The total mass ow (a) and the channel temperature prole (b)as a function of time (0 - 100 s) during high subcooling stable cirulation atP = 1400W/rod, Tsub,exit = 15 K and Kin = 8, 9.

t1 t2 t3 t4

Ch. 1 ↓ G ↓ G

Ch. 2 F ↓ F ↓Ch. 3 ↓ G ↓ G

Ch. 4 ↓ G ↓ G

Table 4.2: The events timetable for in-phase oscillations. Event t2 follows eventt1 within seconds. The time span between t2 and t3 is very long.

in all channels, of which one is shown in gure 4.2b. There is no detectible voidpresent in the chimneys.

4.1.2 In-phase ow oscillations

In the in-phase oscillation regime, all four channels display a ow oscillationat practically the same time. As we can see from gures 4.3c, a mass owoscillation is initiated by a ashing event in one chimney (channel 2 in thiscase, indicated by point A in gure 4.3c). Due to buoyancy, the ow in thischannel is strongly increased. As a result of the inertia of the large amount ofwater in the rest of the natural circulation loop and the local friction experiencedby the ow in the downcomer, this ashing event is enough to cause a smallreverse ow in the other three chimneys, or at least to halt the ow there. Thetemperature of the water in those chimneys, meanwhile, is not far from thesaturation temperature. Since the ow is slightly reversed or halted in thesechannels, the already hot water in the core (or owing back into the core),reaches the saturation temperature shortly after, causing a geysering event inat least one other channel, which is enough to bring the remaining channels togeyser quickly after that.

This is where the story ends for in-phase ow oscillations: although the threegeysering channels also cause a reverse ow in the channel that started the event,

29

t1 t2 t3 t4 t5 t6

Ch.1 F ↓ G ↓ F ↓Ch. 2 ↓ ↓ G ↓ F ↓Ch. 3 ↓ G ↓ G ↓ GCh. 4 ↓ G ↓ G ↓ ↓

Table 4.3: An example of a timetable for behavior in the a-periodical regime.It must be emphasized that the events are not equally separated in time.

it has been ooded with relatively cold water from the channel inlet due to thelarge increase in ow during ashing, as can very clearly be seen in gure 4.3b(point B). Therefore, the reverse ow is not enough to cause another geyseringevent, stabilizing the ow until the next ashing event. As we will see in thenext section, this is the dening dierence between in-phase oscillations andnon-periodical ow oscillations.

The In-phase ow oscillations observed in CIRCUS IV are similar to those foundby Marcel [5] in CIRCUS II. In that case, it was also found that in-phase oscil-lations always start with a ashing event in one of the channels, which subse-quently induces a geysering event in the other channel. It is interesting to seethat in CIRCUS IV the oscillation is still induced by a ashing event in onlyone channel.

4.1.3 A-periodical ow oscillations

A-periodical ow oscillations are also caused by a combination of void ash-ing and geysering events, with the dierence that there is no regular patternanymore. As with in-phase oscillations, the oscillation starts with a void fash-ing event. However, after initiation of a ashing event in one chimney andthe subsequent geysering in the other channels, the temperature in the core ofthe initial channel might now be high enough to cause a subsequent geyseringevent in that channel. Since this new geysering event will again generate reverseow in the other channels, this eect could in principle sustain geysering in allchannels indenetely. Nevertheless, at a certain point in time, this cascade ofgeysering events will be perturbed just slightly (for example by a uctuation inthe inlet temperature or a smaller geysering event in one of the chimneys andthus a smaller reverse ow in the other channels). In that case, the temperaturein the core will not be high enough to initiate a geysering event anymore anda ashing event will follow. It is therefore due to the random nature of theseperturbations and the dierent time scales involved with ashing and geysering,that the a-periocial behavior arises. In table 4.3, an example of a timetable fora-periodical oscillations is shown.

In gure 4.4 such an alternation can be seen. We will follow the event, using theheat and void proles in gures 4.4b and 4.4c, to get a clearer picture of whatis happening. We see that the subsequent geysering events in channels 1 and 2(indicated by A and B respectively), fail to induce a geysering event in channels3 and 4 by reverse ow. As a consequence, the temperature build-up in thosetwo channels starts showing similarities to the in-phase oscillations (indicated

30

1020

3040

5060

7080

9010

011

00

0.1

0.2

0.3

0.4

0.5

0.6

Tim

e [s

]

Total primary flow [l/s]

1020

3040

5060

7080

9010

0−

0.2

−0.

10

0.1

0.2

0.3

0.4

0.5

Tim

e [s

]

Flow [kg/s]

Cha

nnel

1C

hann

el 2

Cha

nnel

3C

hann

el 4

(a)

(b)

(c)

Figure

4.3:Thetotalmass

ow

andthepartialmass

ow

per

channel

(a),thetemperature

proles(b)andvoid

detectiondata

(c)as

afunctionoftimeforin-phase

oscillationatP

=1,

4kW,T

su

b,e

xit

=7,

3°C

andK

in=

8,9.

Thetimeisindicatedin

secondsonthe

horizontalaxes

(10-100)andontheverticalaxes

theaxialpositionofthesensorin

questionisgiven.Thishasbeenclaried

bythe

schem

aticversionsoftheCIRCUSIV

facility

nextto

thepictures.

Note

thatthetemperature

sensors

are

installed

installed

over

the

wholelengthofthesetup,whereasthevoid

sensorsare

only

presentin

thechim

ney.From

leftto

right,theim

ages

representthechannels

1to

4,respectively.

31

by C). At point D, this results in a ashing event in channel 4, completelydisrupting the regular cascade of geysering events that was in place before thebeginning of the time scale. The unpredictable alternation of the geysering andashing phenomena gives rise to the characteristically a-periodical mass owoscillations.

Determination of the a-periodical behavior can be complicated in some cases.Cascades of geysering events can sometimes continue for a long time, especiallyat high power and low subcooling. As a consequence, the recorded signal oftenseems periodical. Increasing the inlet temperature causes these temporary peri-odical oscillations to persist even longer. When, at a certain point, no ashingevents and subsequent distortions of the periodic signal are observed anymorein the measured timeframe (usually 3-5 minutes) , the signal is classied inthe out-of-phase regime. This means that the determination of the a-periodicalregime is limited by the measurement window.

This type of A-periodical behavior has also been found in the CIRCUS II setupby Marcel. He showed that the occurrence of a-periodical behavior may be seenas a cascade of period-doubling oscillation frequency bifurcations, which areimpossible to discriminate from each other. This means that the a-periodicalregime can be thought of as an oscillation frequency transition zone betweenthe very distinct (but dierent) oscillation frequencies in the a-periodical andout-of-phase regimes.

A-periodical oscillations in high-inlet friction conditions

The a-periodical mass ow oscillations described so far, are of the type mostcommonly encountered during experiments. At high inlet friction conditions,however, another type of a-periodical behavior can arise. At these conditions,the reverse ow can become large enough to cause hot coolant from one channelto pass through the lower inlet plenum to another channel. As a result, thetemperature of the coolant directly after a geysering event in a channel, is higherthan it would be if it were only ooded with relatively colder coolant from thedowncomer. The incubation time for the next geysering event in the samechannel will therefore be shorter, disrupting the 'rhythm' of the oscillation. Aswe have seen before, the random perturbations in the magnitude of the reverseow, causes the a-periodical behavior.

Although the oscillations are only caused by geysering and reverse ow, they aredenitely a-periodical. In gures 4.5a and 4.5b, the power spectral densities ofthis type of a-periodical oscillations is compared to the power spectral densityof the (periodical) out-of-phase oscillations (described in the next section). Itcan clearly be seen that in the out-of-phase regime, oscillation occurs at a verydistinct frequency (indicated by the arrow), whereas in the a-periodical regimea wide range of frequencies is found in the signal.

In table 4.4 an example of an oscillation timetable is displayed. At t = t2 thereverse ow rst passes through the common inlet, allowing channels 3 and 4to geyser again, before channels 1 and 2 can. This gives rise to a-periodicalgeysering behavior. Bear in mind that the intervals between t2 − t6 are notregular intervals. This kind of a-periodical oscillation is very similar to some of

32

1020

3040

5060

7080

9010

00.

050.1

0.150.

2

0.250.

3

Tim

e [s

]

Total mass Flow [kg/s]

1020

3040

5060

7080

9010

0−

0.2

−0.

10

0.1

0.2

0.3

0.4

0.5

0.6

Tim

e [s

]

Partial mass flow [kg/s]

Cha

nnel

1C

hann

el 2

Cha

nnel

3C

hann

el 4

(a)

(b)

(c)

Figure

4.4:TheTotalmass

ow

andthepartialmass

ow

per

channel(a),thetemperature

proles(b)andvoid

detectiondata

(c)for

a-periodicaloscillationatP

=1,

4kW,T

su

b,e

xit

=5°CandK

in=

8,9.

Thetimeisindicated

insecondsonthehorizontalaxes

(10-100)

andontheverticalaxes

theaxialpositionofthesensorin

questionisgiven.Thishasbeenclaried

bytheschem

aticversionsofthe

CIRCUSIV

facility

nextto

thepictures.

Note

thatthetemperature

sensors

are

installed

installed

over

thewhole

length

ofthesetup,

whereasthevoid

sensors

are

only

presentin

thechim

ney.From

leftto

right,theim

ages

representthechannels1to

4,respectively.

33

(a) (b)

Figure 4.5: The Power Spectral Densities of a mass ow signal from the a-periodical regime (a) and from the out-of-phase regime (b).

t1 t2 t3 t4 t5 t6

Ch.1 G ↓ ↓ ↓ G GCh.2 G ↓ ↓ G ↓ ↓Ch.3 ↓ G G G ↓ ↓Ch.4 ↓ G G ↓ ↓ G

Table 4.4: High reverse ow a-periodical behavior timetable.

the higher order out-of-phase oscillations that will be described in section 4.1.5.The main dierence is that the reverse ow in that regime occurs on a regularbasis. Moreover, these two regimes are separated by another: the out-of-phaseregime.

4.1.4 Out-of-phase ow oscillations

Continuing to an even lower subcooling domain in gure 4.1, we get to theregime where regular, sinusoidal oscillations are encountered. These oscillationsare called out-of-phase because they typically involve the alternation of twochimneys displaying a geysering event and a reverse ow in the other two, as canbe clearly seen in gure 4.6a. Whereas in the a-periodical regime, a periodicalcascade of geysering oscillations could only be temporarily maintained, this isnot the case in the out-of-phase regime. The oscillations in this regime alwaysremain periodical, even after disturbing the power or friction in one or morechannels. The oscillations in this regime are only caused by geysering and reverseow. Flashing is not encountered anymore. This is a very distinct dierencebetween the geysering/ashing-induced a-periodical oscillations, which will bevery useful in the prediction of the stability boundaries between the regimes inchapter 5. The oscillation timetable is given in table 4.5.

The described oscillation is very similar to the out-of-phase behavior found byMarcel [5] in CIRCUS II. Even more so because of the two-by-two pairing of

34

010

2030

4050

6070

0

0.050.

1

0.150.

2

0.250.

3

0.350.

4

Tim

e [s

]

Total mass Flow [kg/s]

010

2030

4050

6070

−0.

2

−0.

10

0.1

0.2

0.3

0.4

0.5

Tim

e [s

]

Flow [kg/s]

Cha

nnel

1C

hann

el 2

Cha

nnel

3C

hann

el 4

(a)

(b)

(c)

Figure

4.6:TheTotalmass

ow

andthepartialmass

ow

per

channel(a),thetemperature

proles(b)andvoid

detectiondata

(c)for

out-of-phase

oscillationatP

=1,

4kW,T

su

b,e

xit

=0,

6°C

andK

in=

8,9.

Thetimeisindicatedin

secondsonthehorizontalaxes

(0-

70)andontheverticalaxes

theaxialpositionofthesensorin

questionisgiven.Thishasbeenclaried

bytheschem

aticversionsofthe

CIRCUSIV

facility

nextto

thepictures.

Note

thatthetemperature

sensors

are

installed

over

thewholelength

ofthesetup,whereasthe

void

sensors

are

only

presentin

thechim

ney.From

leftto

right,theim

ages

representthechannels1to

4,respectively.

35

t1 t2 t3 t4

Ch.1 G ↓ G ↓Ch.2 G ↓ G ↓Ch.3 ↓ G ↓ GCh.4 ↓ G ↓ G

Table 4.5: The oscillation timetable for out-of-phase oscillations. In this case,the events are equally separated in time.

t1 t2 t3 t4 t5

Ch.1 G - ↓ G ↓Ch.2 ↓ G ↓ G ↓Ch.3 ↓ ↓ G ↓ GCh.4 ↓ ↓ G ↓ G

Table 4.6: The channel pairing process for out-of-phase oscillation, as suggestedby the author. Events t1 and t2 occur at practically the same time, while thetime spans between t2, t3, t4 and t5 are larger.

the geysering channels. An explanation for this pairing eect does not seem tobe straightforward. It is speculated by the author, that the pairing is due tothe fact that one geysering event does not induce a large enough reverse owto postpone geysering in all other channels. This idea can be made clear whenwe have a look at table 4.6. At t = t0 we turn on the power in the system.All channels will heat up at the same pace, but due to small perturbations onechannel will always display a geysering event rst (at t1). Due to this event,there is a (small) equal reverse ow in all the other channels, pushing back hotcoolant into the core. Shortly after, at t2, one of the remaining three channelswill display a geysering event, adding to the reverse ow in channels 3 and 4.At this point, the total reverse ow in those channels has been enough to pushall the hot coolant from the core. After the two geysering events, the naturalcirculation brings the hot coolant back to the cores of channels 3 and 4 and att3 a simultaneous geysering event will follow. This, in turn, causes a reverseow in channels 1 and 2 that is high enough to push the hot coolant from theircores. This way a two-by-two out-of-phase oscillation is achieved.

The pairing of the channels could be an interesting topic for further research,since it makes quite a dierence in large multi-channel systems whether thegeysering events are spread out in time, or display the same pairing behavior.In the former case, the total ow through the system will probably not vary farfrom its standard value, but if the channels start displaying a 10 vs. 10 or a500 vs. 500 out-of-phase oscillation, this could have severe consequences for themass ow.

4.1.5 Higher order out-of-phase ow oscillations

At even lower subcooling and high power, a regime was observed in which arange of more exotic oscillations can be observed. Most of them include states

36

t1 t2 t3 t4

Ch.1 G G G G

Ch.2 G G G G

Ch.3 ↓ ↓ ↓ ↓Ch.4 ↓ ↓ ↓ ↓

(a)

t1 t2 t3 t4

Ch.1 G ↓ G ↓Ch.2 G ↓ G ↓Ch.3 ↓ G ↓ G

Ch.4 ↓ ↓ ↓ ↓(b)

t1 t2 t3 t4

Ch.1 G G G G

Ch.2 G G G G

Ch.3 G G G G

Ch.4 ↓ ↓ ↓ ↓(c)

t1 t2 t3 t4

Ch.1 G ↓ ↓ ↓Ch.2 ↓ G ↓ ↓Ch.3 ↓ ↓ G ↓Ch.4 ↓ ↓ ↓ G

(d)

Table 4.7: Oscillation timetables for some of the higher order out-of-phase os-cillations. In all cases the interval between consecutive events is equal.

in which only reverse ow is detected in some channels and only geysering inother channels. Among the most important of the recorded oscillations are:

Two periodically geysering channels in combination with only periodicalreverse ow in the other channels (2 vs. 2 reverse, see table 4.7a).

Geysering in two channels alternating with geysering in one other channel,combined with only reverse ow in the last channel (2 vs. 1 vs. 1 reverse,see table 4.7b).

Three simultaneously geysering channels in combination with a simulta-neous reverse ow in the last channel (3 vs. 1 reverse, see table 4.7c).

All four channels geysering separately at equal time intervals (1 vs. 1 vs.1 vs. 1, see table 4.7d).

In gure 4.7, for example, a 2 vs. 2 oscillation state is shown. From gure4.7a, it becomes clear that there is a large reverse ow in channels 2 and 4 ateach geysering event in the other channels. In this situation, the reverse owhas become large enough push all the hot coolant from the core sections of thenone-geysering channels, as can be clearly seen from the downward slope in thetemperature proles at points A. This also means that hot coolant is insertedinto the core of the geysering channels via the inlet, thus enabling them to reachthe saturation temperature again before the reverse ow channels do. This waythe oscillation is maintained.

Due to the fact that most of the oscillations in this regime are either linkedto the presence of four parallel channels or occur only at high common inletfriction, the higher order out-of-phase regime was not observed in CIRCUS II.

37

010

2030

4050

600.

050.1

0.150.

2

0.250.

3

Tim

e [s

]

Total mass Flow [kg/s]

010

2030

4050

60−

0.3

−0.

2

−0.

10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tim

e [s

]

Partial mass flow [kg/s]

Cha

nnel

1C

hann

el 2

Cha

nnel

3C

hann

el 4

(a)

(b)

(c)

Figure

4.7:TheTotalmass

ow

andthepartialmass

ow

per

channel(a),thetemperature

proles(b)andvoid

detectiondata

(c)for

2vs.

2reversehigher

order

out-of-phase

oscillationatP

=2,

2kW,T

su

b,e

xit

=0°C

andK

in=

8,9.

Thetimeisindicatedin

seconds

onthehorizontalaxes

(0-60)andontheverticalaxes

theaxialpositionofthesensorin

questionisgiven.Thishasbeenclaried

by

theschem

aticversionsoftheCIRCUSIV

facility

nextto

thepictures.

Note

thatthetemperature

sensors

are

installed

over

thewhole

length

ofthesetup,whereasthevoid

sensors

are

only

presentin

thechim

ney.From

leftto

right,theim

ages

representthechannels1to

4,respectively.

38

4.1.6 Low subcooling stable ow

Inter-channel circulation

At very high power and low subcooling conditions, another stable mass owregime emerges, as shown in gure 4.1. Although similar, it is not exactly thestable ow previously found in a single chimney setup by Manera [4] and Marcel[5]. In those cases, both a single phase as a two-phase region was present in thechimney, separated by a relatively stable ashing boundary. CIRCUS IV showscomparable behavior, but not for all chimneys equally. As we can concludefrom the partial mass ow in gure 4.8a, continuous inter-channel circulationis present in the system at these conditions.2 There are two stable ashingchimneys (channel 2 and 4 in this case), and two channels in which there is onlya continuous reverse ow.

To clarify, we will have a look at the characteristics of a typical low subcoolingstable ow in gure 4.8. The stable situation is initiated by a simultaneousgeysering event in channels 2 and 4 (indicated as point A). During this event,the reverse mass ows in channels 1 and 3 become large enough to feed hotcoolant from their cores to the inlets of the other two (already ashing) chan-nels, which allows them to remain in a continuous ashing state. The exampleshown, is recorded at high common inlet friction (Kin = 370), because it isclear that the large friction in the downcomer has a signicant inuence on theexistence of inter-channel circulation, since the ow through the primary loopis in continuous competition with reverse ows in a part of the the channels.

Hysteresis

Once the system has been brought into this low subcooling stable ow regime,part of the hot coolant will be recirculated between channels. To keep it intothis state, the inlet temperature does therefore not need to be as high as itwas when the behavior was initiated. The same can be said for the power:less power is needed to sustain the process than to initiate it. This meansthat the low subcooling stable ow has, in fact, two boundaries in the power-subcooling plane: an initiation boundary and a maintenance boundary. In gure4.9, the eect is shown schematically. Starting from the operational point atpoint A, which could be in the out-of-phase oscillation regime for example, weslowly decrease the inlet subcooling until the low subcooling stable ow regimeis initiated at point B. This means that the initiation boundary of this regime isat point B. Now, if we decrease the inlet temperature again, the system will stayin the stable ow regime, even though less heat is added to the system. It mightreturn to the out-of-phase regime at point A, or even at point C. This point iscalled the maintenance boundary, since it indicates how much energy needs tobe added to the system to maintain the stable regime. The stability behavioris consequently dierent depending on whether we are increasing or decreasingthe inlet temperature. This eect is called hysteresis. The dierence between

2Although we are dealing with stable mass ow, the pressure drop over a channel in theseconditions are high enough to calculate the partial mass ows with relatively small uncertainty(see section 3.4).

39

020

4060

8010

00

0.02

0.04

0.06

0.080.

1

0.12

0.14

0.16

0.180.

2

Tim

e [s

]

Total mass Flow [kg/s]

020

4060

8010

0−

0.2

−0.

10

0.1

0.2

0.3

0.4

0.5

Tim

e [s

]

Partial mass flow [kg/s]

Cha

nnel

1C

hann

el 2

Cha

nnel

3C

hann

el 4

(a)

(b)Tem

perature

prolesforeach

channel.

(c)Void

detectedin

thechim

ney

section.

Figure

4.8:TheTotalmass

ow

andthepartialmass

ow

per

channel(a),thetemperature

proles(b)andvoid

detectiondata

(c)for

lowsubcoolingstableow

atP

=1,

8kW,T

su

b,e

xit

=1,

2°CandK

in=

370.

Thetimeisindicatedin

secondsonthehorizontalaxes

(0-

100)andontheverticalaxes

theaxialpositionofthesensorin

questionisgiven.Thishasbeenclaried

bytheschem

aticversionsofthe

CIRCUSIV

facility

nextto

thepictures.

Note

thatthetemperature

sensors

are

installed

over

thewholelength

ofthesetup,whereasthe

void

sensors

are

only

presentin

thechim

ney.From

leftto

right,theim

ages

representthechannels1to

4,respectively.

40

Figure 4.9: The concept of hysteresis in CIRCUS IV.

the two boundaries can be quite large and, as we will later see, a disturbance(e.g. a friction or power distribution between the channels) can be enough toattain the low subcooling stable state far below the initiation boundary.

The question might arise why no hysteresis has been found in the higher orderout-of-phase ow regime. This is due to the fact that, contrary to the stableow regime, in none of the observed oscillation states in the higher order out-of-phase regime, the inter-channel recirculation is permanent. At the moment thereverse ow stops, colder coolant will be fed to the channels from the commoninlet.

At this point, we can get back to the remark made with respect to the lowsubcooling stable ow regime in gure 4.1. At a low common inlet friction coef-cient (Kin = 8, 9), this regime has been recorded, but its (initiation) boundarycould not be determined. This is due to the fact that the regime was invoked bydisturbing the higher order out-of-phase regime by temporarily increasing thecommon inlet friction in that case. After the stable ow regime was initiated,the friction was brought back to its original value. Nevertheless, the regime wasmaintained. Apparently, we can conclude that although the initiation bound-ary was not yet reached in the CIRCUS IV measurable range, the maintenanceboundary was. As a result, the regime could be recorded under low commoninlet friction conditions.

4.2 The stability map

The occurrence of the instabilities described in the previous section can beindicated in the power-subcooling plane. The resulting map, called a stabilitymap, is shown in gure 4.10 for two dierent values for the common inlet friction

41

coecient. The colored lines are second order polynomial ts for the set ofhighest subcooling data points of each regime. They indicate the approximateboundaries between the dierent regimes. In the low inlet friction stabilitymap (gure 4.10a), ve regimes can be found. Starting at high subcooling andincreasing it as in gure 4.1, we pass from the stable ow regime to higher orderout-of-phase oscillation states. In gure 4.10b, we encounter the same regimes,plus the low subcooling stable ow regime.

The most likely path that will be taken during the startup of a reactor, isslowly increasing the coolant temperature until enough vapor can be createdto pressurize the system. As a result, the low subcooling stable regime willnot be encountered until the initiation conditions are met. For this reason, theinitiation boundary was chosen as the dening boundary for the low subcoolingstable regime. This is the reason why this regime is not found in the low commoninlet friction stability map.

One thing we notice in gure 4.10, is that the upper stability boundaries seemsto pass the horizontal Tsub = 0K axis at approximately 450 W in both cases. Itis expected that this is caused by the heat loss and evaporation in the channels,since, at zero subcooling, boiling would occur at the top of the chimney if noheat were lost in the system. The approximate location at which the horizontalaxis is crossed, is therefore an indication of the heat loss in the core and chimneysections. This value is comparable with our estimate of the heat loss over thecore in section 3.7.

4.2.1 The inuence of the common inlet friction coecient

It immediately becomes clear from the gures 4.10a and 4.10b, that the commoninlet friction has a large inuence on the stability of the system. At Kin = 370,the system becomes much more unstable: Instabilities are already observedat a much higher subcooling (or lower power). This eect had been expectedbeforehand; when the friction of the natural circulation loop was increased, adecrease of the ow through the system followed, which means that more heatcan be transferred to the coolant in the core for the same inlet temperature andpower conditions. It is due to the shifting stability boundaries at higher inletfriction coecients that we have been able to study the higher order out-of-phaseregime and the low subcooling stable regime in more detail.

One thing we also notice, is that the relative size of the out-of-phase regime hassignicantly decreased. This eect is caused by the increased reverse ow athigh common inlet friction, as can be seen in gure 4.11. The data in this gurehas been acquired by comparing the time averaged reverse ow to the upwardow in the channels for a large number of geysering events:

Relative reverse ow =

´ t2t1Mupdt´ t2

t1Mreversedt

(4.1)

where t1 and t2 mark the start and the end of the geysering event. From theinformation in the gure it becomes clear that at higher inlet friction coecients,the reverse ow is relatively much higher than at low inlet friction. Due to the

42

0.5 1 1.5 2

0

2

4

6

8

10

12

14

16

18

20

Power/rod [kW]

Sub

cool

ing

[K]

Stable flowIn−phase osc.A−periodical osc.Out−of−phase osc.Higher order osc.

(a)

0.5 1 1.5 20

5

10

15

20

25

30

35

40

45

50

Power/rod [kW]

Sub

cool

ing

[K]

Stable flowIn−phase osc.A−periodical osc.Out−of−phase osc.Higher order osc.Low subc stable flow

(b)

Figure 4.10: The stability maps: (In)stability behavior in the power-subcoolingplane for Kin = 8, 9 (a) and Kin = 370 (b). Subcooling has been taken relativeto conditions at the chimney outlet. The vertical axes in these images are notat the same scale.

43

84 86 88 90 92 94 96 980

0.1

0.2

0.3

0.4

0.5

0.6

Inlet temperature

rela

tive

reve

rse

flow

Kin=370 P=1,4kWKin=370 P=1,8kWKin=8,9 P=1,8kWKin=8,9 P=2kWKin=8,9 P=2,2kW

Figure 4.11: The reverse ow relative to the upward ow in geysering channelsfor high and low inlet frictions.

increased reverse ow, the hot coolant can already be removed from the corecompletely at much higher subcooling, hence giving rise to higher order out-of-phase oscillations, in which this eect plays an important role, as we have seenin section 4.1.5.

4.3 Comparison of the stability behavior of the

dierent CIRCUS setups

One of the goals of this thesis is to study the eect of chimney division onstability. Now that we have acquired stability information on all three CIRCUSsetups, we can proceed to combine the results to make some statements aboutchimney division.

4.3.1 Comparability

As described in chapter 3, the geometry of the CIRCUS IV setup is slightlydierent than its predecessors. Before we can compare the stability behaviorin the dierent CIRCUS geometries, we will therefore study the eects of thesedierences on the stability of the setups and emphasize the issues that have tobe taken into account during the comparison.

Chimney height

Since the chimney is approximately 50 cm taller in CIRCUS IV, it is expectedthat the mass ow through the facility will increase due to the additional pres-sure head. The resulting larger ow will give the coolant less time to heat up in

44

50 55 60 65 70 75 800

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Buffer Level [cm]

Ave

rage

mas

s flo

w [k

g/s]

Stable FlowOut of phase flow

Normal operational level

Figure 4.12: The average ow in the stable ow regimes for varying buer levelheights at P = 1, 4kW and Kin = 8, 9.

the core and therefore it is expected that CIRCUS IV will be more stable thanit would be with a shorter chimney.

However, the interactions between gravitational pressure head, the heat trans-fer in the core and the friction in the system are not always straightforward:a smaller amount of heat transferred in the core will, in turn, have a negativeeect on the thermal driving head, because of the decrease in density dier-ence between the downcomer and the heated channels. For this reason, someexperiments are conducted with a varying buer level in CIRCUS IV. Duringoperation in the high subcooling stable ow regime and the out-of-phase owregime, the buer level was decreased and increased around the standard op-erational level. It was found that for a xed power and inlet temperature, avariation of the buer level did not signicantly increase the ow through thesystem, see gure 4.12. This is an indication that, in contrast to our expecta-tion, the height increase of approximately 50 cm will probably not have a verylarge inuence on the mass ow through the system.

Another eect we can expect with a taller chimney, are larger pressures in thesystem due to the additional static pressure. The density (and consequently theenthalpy) are nonetheless hardly dependent on the pressure in the operationalrange of the facility, therefore it is expected that this eect can be neglected.

Downcomer friction

Due to the decrease of the downcomer diameter (half of what it was in CIRCUSI and II, see table 3.1), the velocity of the downward ow is relatively higher. Asa result, the Reynolds number will be twice as high at equal mass ow throughthe system. Considering that all CIRCUS setups are displaying turbulent owin the downcomer throughout practically the whole measureable range, this will

45

decrease the friction coecient in this section.3 Nevertheless, since the totalfrictional pressure drop scales with the square of the velocity (see equation 3.1),the pressure drop due to friction will be higher at the same mass ow. We canconclude from this that a decrease in downcomer width will generally cause thenatural circulation loop to settle at a lower ow equilibrium if the same amountof energy is added to the system. The eect on stability will be similar to thesituation with a high inlet friction coecient explained in section 4.2.1 (onlymuch less drastic).

Inertial eects

It was found for CIRCUS I by Manera and Van der Hagen [22], that the re-lationship between driving pressure in the loop and kinetic pressure can beapproximated by a straight line passing through the origin and that the staticcharacteristics are well correlated regardless of whether the ow condition isstable or unstable. This means that in both stable and unstable circulation, thedriving pressure and the friction are the major terms in the integrated momen-tum balance over the loop and that inertia does not play a major role.

It has also been found by Manera and Van der Hagen [22] and by Marcel [5],that inertia does invoke a phase lag between the void fraction in the chimneyand the ow rate through the system. In the CIRCUS IV setup, the inuence ofinertia is not expected to dier much from the previous setups, because the totalamount of coolant present in the system is approximately the same after thegeometrical alterations. To test this, the cross correlation of the void detectionsignal and the corresponding mass ow characteristic is calculated and shownin gure 4.13. It can be seen that there is indeed a delay of approximately 0,6 sdue to inertia. This corresponds well to the 0,77 s found by Marcel in CIRCUSII.

Nevertheless, this inertia eect is not expected to inuence the position of thestability regimes themselves. The stability behavior is dependent on steadycharacteristics like the inlet temperature and the power. Although inertia mayinuence the ow characteristics during unstable ow, it will not determine atwhich conditions unstable ow occurs.

Cross-sectional area

In table 3.1 it can be seen that the total cross-sectional area of the CIRCUSIV chimneys is 8% larger in comparison to CIRCUS I. At equal mass ow, thiswould result in a decrease of velocity in the chimneys4 Since the ow throughoutboth setups remains in the turbulent regime during single phase circulation anddierence in cross-sectional area is not that large, no signicant wall frictioneect on the ow (and consequently the stability of the system) is expected bythis small velocity increase.

3As can be seen in the Moody diagram. See for example [20]4The core section is unchanged, so at equal mass ow, the velocity in the core and also the

heat transferred to the water, remains the same.

46

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

Tau [s]

CC

F [−

]

Figure 4.13: The correlation of recorded signals from the void detection (thedriving force) and the corresponding mass ow in channel 1 during in-phaseoscillation at P = 1400W and Tsub = 9, 5.

4.3.2 Increase of chaotic behavior

Now that we have emphasized some of the comparability issues that have to bekept in mind, the rst thing we can do, is simply compare the stability mapsof the dierent CIRCUS setups in the power-subcooling plane in a qualitativemanner. The rst remark we can make is that in this plane, the CIRCUS IVsetup seems to be the most stable one. 5

Although the peripheral systems of CIRCUS I and CIRCUS II are essentially thesame, the former is much more unstable as a result of the fact that measurementswere conducted with a high local friction in the downcomer.6 Extensive analysisof the data recorded by Manera [4], shows that the K-factor associated with thelocal frictional pressure drop is approximately K = 128.

Another thing we can conclude from gures 4.14a to 4.14c, is that the a-periodical regime has increased with the division of the chimney into separateparallel channels. From no reported a-periodical oscillations in CIRCUS I,7 toan a-periodical region at high power in CIRCUS II to a large a-periodical transi-tion zone between the in-phase and out-of-phase oscillations. Since we have seenthat reverse ow plays a role in the occurrence of a-periodical oscillations, it isnot surprising that the behavior was not found in CIRCUS I; it simply has noparallel channel in which a reverse ow can be induced. The question remains,however, why no a-periodical transition was found in CIRCUS II between the

5Be aware that we are still comparing systems with several peripheral dierences, as wehave just noticed in the last section. At this stage, we may not conclude that systems withfour parallel channels are generally more stable than systems with two parallel channels.

6From personal communication with Annalisa Manera.7No a-periodical oscillations were reported by Manera [4], although a study by Clausse

and Lahey [23], based on a analytical, non-linear model, shows that, theoretically, a-periodicalbehavior could be possible in a single channel as a cascade of oscillation frequency bifurcations.

47

(a) CIRCUS I

(b) CIRCUS II

(c) CIRCUS IV

Figure 4.14: The stability maps for the dierent CIRCUS congurations.Sources: Manera [4], Marcel [5]. The vertical axes in the gures dier in scale.The respective stability lines have been drawn by the respective authors them-selves.

48

in-phase and out-of-phase regions for relatively low power. It could be due tothe fact that the reverse ow in these regions was very small, causing the a-periodical region in the stability map to be too small to be measured. Anotherpossible explanation is that a-periodical oscillations were accidentally confusedwith out-of-phase oscillations, due to the occurrence of relatively longer inter-vals of periodical oscillations in these conditions.8 More investigation into thea-periodical behavior in CIRCUS II is needed to account for this observation.Unfortunately, the measurements conducted with the CIRCUS II setup in thisoperational range could not be retrieved.

4.3.3 Overall stability

In the previous sections, we have compared systems in the power-subcoolingplane. These are not the only parameters that play a role in the comparisonof systems, however. Due to friction dierences, for example, dierent massows are induced by natural circulation at the same power and inlet tempera-ture conditions. As we have seen before, the ow also inuences the stabilitycharacteristics of the system. It is therefore more logical to compare the sys-tems in the dimensionless Npch-Nsub plane, in which all relevant parameters aretaken into account. The stability measurements from gures 4.10a and 4.10bare translated to this plane using the following relations:

Npch =P

Mhfg

ρl − ρv

ρv(4.2)

Nsub =hl,sat,ci − hl

hfg

ρl − ρv

ρv(4.3)

Where P is the applied power in the core, Ac the core cross sectional area, Mthe (time-averaged) primary mass ow, hl,sat,ci, hl and hfg are, respectively,the liquid saturated enthalpy at the core inlet, the liquid enthalpy at the coreinlet and the specic vaporization enthalpy and ρl and ρv are the liquid andvapor density of the coolant.

In gure 4.15a the upper stability boundaries (i.e. the transitions from high-subcooling stable ow to the in-phase oscillation regime) are shown in the Npch-Nsub plane. For easier comparison to the data presented by Marcel [5], thesubcooling number has been determined with respect to the core inlet saturationenthalpy. Since CIRCUS IV is taller than its predecessors, the pressure and asa consequence the core inlet saturation enthalpy at its inlet are slightly higher.To enable comparison of the systems, the CIRCUS IV data displayed in gures4.15a and b, has therefore been corrected for this eect, by calculating thecore inlet subcooling with respect to the saturation enthalpy at the inlet of theCIRCUS II setup. Two straight lines are also shown in gure 4.15. These linesrepresent zero quality at the exit (Npch = Nsub,re) and zero quality at the inlet(Npch = Nsub,ci) of the CIRCUS II facility.

It is clear that all stability boundaries in gure 4.15a are located below thesaturation line corresponding to zero quality at the chimney exit. It is expected

8We have discussed in section 4.1.3, that the measurement window plays a role in makinga distinction between the a-periodical and the out-of-phase regimes.

49

(a) The upper stability boundaries of all three CIRCUS setups and CIRCUS IIoperating at 1 channel for Kin = 8, 9.

(b) The high and low subcooling stability boundaries at high inlet friction for CIR-CUS II (operating at 1 channel and Kin = 340) and CIRCUS IV (Kin = 370).

Figure 4.15: Stability boundaries for the dierent CIRCUS congurations in theNpch-Nsub plane.

50

that this eect is partly caused by heat loss from the system and partly bythe production of vapor in the channels. The important implication for theESBWR is that the reactor can be started up in the high subcooling stablenatural circulation regime, while also producing vapor to pressurize the system.

Although, the data in gure 4.15a does not seem to form a neat curve, oneconclusion that can be drawn from it, is that the CIRCUS IV upper stabilityboundary displays a shift towards the Xre = 0 line at higher subcooling num-bers, with respect to the CIRCUS II stability boundaries in both the double andsingle channel coguration. This means that the high subcooling stable regimeat these operational points becomes smaller and the unstable operating rangebecomes larger compared to the CIRCUS II setup (in both single and doublechannel setup). At lower subcooling numbers however, we see an opposite trend.The CIRCUS IV stability boundary is further away from the Xre = 0 line thanthe CIRCUS II stability boundaries. The eect could possibly be caused by anincreased heat loss in CIRCUS IV at the low subcooling, and low power overow conditions at these operational points. It must also be emphasized thatthe uncertainty in the determination of Npch has become relatively large in thisdomain, due to the high relative uncertainty in the determination of the massow at low the corresponding low mass ow conditions. More information aboutthe determination of the uncertainty in Npch can be found in appendix C.

For CIRCUS I, a dierent pattern is observed. Its stability boundary is locatedat higher phasechange numbers, due to the increased K-factor in the down-comer and the resulting lower mass ow through the system. Due to the factthat only few data points are available and because they are spread out in thedimensionless plane, it is questionable to draw conclusions from the comparisonwith the CIRCUS IV and CIRCUS II stability boundaries.

When we compare gure 4.15a to gure 4.15b, we notice that a larger commoninlet friction causes the stability boundaries to deviate from the chimney outletzero quality line (Xre = 0). Also, the data is stretched out in the directionof higher phasechange numbers. The position of the upper boundaries leadsus to conclude that, at the same operational point, the setup becomes moresstable when a high common inlet friction is applied. A small dierence can alsobe noticed between the upper and lower stability boundaries of CIRCUS IV atKin = 370 and CIRCUS II (1 Ch.) at Kin = 340. However, the two systems aretoo dierent to point out if this small shift is caused by the additional frictionin CIRCUS IV, the dierence in heat loss in the system, or another eect.

In addition to the location of the stability boundaries, it is interesting to inves-tigate if the whole unstable area (i.e. the unstable area between the upper andthe lower stability boundary) of the setup would widen by adding friction to thesystem, or if it would just display a shift in the Npch-Nsub plane. As a reference,the CIRCUS I stability boundaries, which were observed at intermediate com-mon inlet friction coecient (K = 128), have been added to gure 4.15b. Sincethe low subcooling stable circulation state is only attained in high common inletfriction conditions, the only other comparison we have in this respect, are ex-periments conducted by Marcel [5] at the CIRCUS II setup, with one chimneyclosed o. No high common inlet friction measurements were conducted withthe CIRCUS II double channel setup, nor was the low subcooling stable regimedetected in this conguration. Comparison of the six stability boundaries in

51

gure 4.15b results in the conclusion that although the whole unstable regimeseems to stretch out in the direction of higher phasechange numbers, the mainresult of adding friction to the system is a shift away from the zero quality atthe chimney exit line. This means that the high subcooling stable regime isenlarged at these conditions. However, due to the fact that the low subcoolingstable regime lies largely outside and at the edge of the CIRCUS measurementrange, only few data points are available to base this conclusion on. Therefore,we will try a dierent approach in the next chapter.

52

Chapter 5

Simulation and verication

5.1 Theoretical model

In the introduction, the ashing phenomenon was explained and identied asthe primary cause of instabilities at low pressure and low power conditions. Fora ashing event to occur, the temperature of the coolant in the chimney mustreach the local saturation temperature. If we assume the pressure prole overeach channel to be linear, the lowest saturation temperature can be found at thetop of the chimneys. When, consequently, the coolant inlet temperature is slowlyincreased during operation in the high subcooling stable regime, it can thereforebe expected that the rst ashing-induced instabilities will approximately beencountered at the moment coolant at the core exit saturation temperaturereaches the top of the chimney. Using this information, it will be possible tocreate a simple analytical model to predict at which power and inlet temperatureconditions the ashing eect is rst encountered.

Just before the onset of instability, the ow would be stable. This allows foran analytical approach from the steady state perspective. Starting from themomentum balance:

dρudt

+ u∇ρu = −∇p+ ρg − Ff (5.1)

where Ff is a model for the circumferentially averaged wall shear stress andlocal frictional pressure drops. It can be described by:

Ff =12ρKiu2δ(l − li) +

12ρu2 f

D(5.2)

where f is the friction factor related to wall friction, D the diameter of thepipes and Ki the friction coecient for localized contributions to the pressuredrop.1 For steady state circulation, the inertia term disappears. If we integrate

1Although the symbol f is often used to indicate the Fanning friction factor, it is notthe case here. In this thesis, the Darcy friction factor is used. The dierence is a factor 4:f = 4ffanning .

53

this equation over the whole closed loop, the pressure term and the convectiveacceleration term drop out. We are left with˛

ρgdl =˛

Ffdl (5.3)

where the contour integrals are used to indicate integration over the closed loop.Working out the gravity term (the thermal driving head term), gives

˛ρgdl =

H

0

〈ρch〉gdz +

0ˆ

H

〈ρdc〉gdz

= 〈ρch〉gH − 〈ρdc〉gH = ∆ρgH (5.4)

Where H is the height of the facility, 〈ρch〉 the average density of the coolant inthe heated channel and 〈ρdc〉 the average density of the coolant in the downcomerchannel. Since the setup consists of sections of dierent geometries, we cansplit up the frictional pressure drop term into several components, one for eachsection:

∆p = ∆p1 + ∆p2 + ...+ ∆pn

=n∑

i=1

12ρiKiu

2i +

n∑j=1

12fj

(uj)2

Djρj lj (5.5)

=12

n∑i=1

ρi

(Ki + fi

liDi

)u2

i

Where, in the last term, all the localized frictional pressure drops in each sectionhave been combined. Combined, the two terms in equation (5.3) provide us withthe following relation:

∆ρgH =12

n∑i=1

ρi

(Ki + fi

liDi

)u2

i (5.6)

Secondly, we can compose an energy balance for the steady state situation. Forthis we assume that the heat ux from the electrically heated rods in the core isconstant and axially uniform. We also neglect variations in the inlet subcoolingand enthalpy variations with pressure. If we assume that all power applied tothe heating rods is absorbed by the coolant, the energy balance simply becomes:

∆h =q

M=

q

ρcucAc(5.7)

where ∆h = hc,out − hc,in is the enthalpy change in the core, q the applied corepower and M the mass ow through the system. ρc, uc and Ac are respectivelythe density, coolant velocity and cross-sectional surface area in the core. Wehave seen that there is a signicant heat loss from the channels. Equation 5.7therefore becomes:

∆h =(q + qloss)ρcucAc

(5.8)

54

Where qloss is introduced as the heat loss.

Making use of the equations (5.6) and (5.7), a stability boundary can be cal-culated. From a given hin (Tin) and the fact that the enthalpy of the coolantexiting the core must be equal to the saturation enthalpy at the top of the chim-neys (hsat,re), we can calculate ∆h. Using equation (5.7), we have established arelation between hin and the applied power necessary to initiate ashing at thisinlet enthalpy, q: Exactly the information we would need to draw the stabilityline in the power-subcooling plane. After a value for uc is obtained throughequation (5.6), q can be calculated. The relation for the stability boundarybecomes:

q =hsat,re − hin

ρcAc

√√√√√ 12

n∑i=1

ρ(Ki + fi

liDi

)∆ρgH

− qloss (5.9)

For the calculation of the coolant density throughout the system, the XSteamMatlab package is implemented. We see from equation (5.9), that to be able tocalculate the stability boundary, expressions for the friction coecients in thesystem must be known, which is the subject of the next section.

As we are modeling a single phase, steady state system, there is no reason whywe could not extend the single channel situation to multiple parallel channels,as long as we adjust for the additional wall friction due to channel division.

5.2 Friction

The calculation of the friction in the setup is one of the most important parts ofthe model. We can experimentally determine the K-factors, that are related tothe concentrated frictional pressure drops of valves, bends, inlets etc., over theparts of the setup where dierential pressure sensors are present. This can bedone, for example, at the chimney exit, the core inlet channels and the commoninlet friction valve (see gure 3.2). The other friction factors will have to beevaluated by means of standard geometry-based correlations.2 An overview ofthe measured and calculatedK-factors can be found in table 5.1, the descriptionsrefer to the schematic of CIRCUS IV in gure 3.2.

For the wall friction coecients, expressions are available in the literature.3 Atlaminar ow conditions, the Darcy friction factor is given by:

f =64Re

(5.10)

and in turbulent conditions, an approximation of the friction factor for a fullowing circular pipe was given by Haaland [24]:

1√f

= −1, 8log10

[(ε/D

3, 7

)1,11

+6, 9Re

](5.11)

2See for example Dekkers and Wijnen [26] or Idelchik [27].3See for example Todreas and Kazimi[28].

55

Section K-factor

Common inlet valve 8,9Channel inlet (valves & bends) 3,45

Chimney outlet 1,7Pre-heater vessel 0,7Buer vessel 0,4

Expansion vessel 1,2Left bottom bend 0,15

Total 16,5

Table 5.1: Measured and calculated friction coecients in the CIRCUS IV setup.

A convenient relationship that incorporates both the laminar and turbulent owregimes with a transition to turbulent ow at Re = 2100 is that of Churchill:4

f = 8

[(8Re

) 112

+ (a+ b)−32

] 112

(5.12)

With:

a =

[2, 457ln

((7Re

)0,9

+ 0, 27ε

D

)]16

(5.13)

b =(

37530Re

)16

Notice that, since the wall friction coecient depends on the ow velocity (theReynolds number), we will have to conduct an iteration with equations (5.6)and (5.12), to nd the velocity in the system.

5.3 Modeling of the out-of-phase and a-periodical

stability boundaries

The prediction of the upper (in-phase) stability boundary is not the only onethat can be predicted by the simple model discussed in section 5.1. Whilestudying the instability phenomena in chapter 4, we noticed that one of thedening characteristics of the unstable regimes in the stability map is the lo-cation of vapor production. In-phase ow oscillations are driven by ashing,whereas out-of-phase oscillations are caused by geysering. During a-periodicaloscillations both phenomena play a role.

Another way to formulate this conclusion for the out-of-phase regime specically,is that an out-of-phase situation can only be sustained indenitely if geyseringcan always occur. This is an observation we can easily turn into a requirementsimilar to that for the upper stability boundary, by setting the enthalpy of the

4See for example Oliemans [25].

56

coolant leaving the core equal to the saturation enthalpy at the core exit. Byusing the described model, we apply the simplication that geysering occurs insteady state conditions. This is a simplication of reality, but admissible sincewe are only trying to calculate at which power and inlet temperature conditions,geysering must happen, not when it occurs in dynamic conditions.

For the a-periodical regime, things are a little more complicated. We have seenthat the dening characteristic for the occurrence of a-periodical behavior isreverse ow. As long as a large enough reverse ow is induced during geyseringor ashing events, a cascade of geysering events can be sustained indenitely.In practice, however, this cascade will sooner or later "miss a step" due toa certain perturbation and leave room for a ashing event. The reverse owcan be experimentally determined in CIRCUS IV (see for example gure 4.11),but it has at the same time shown to be highly dependent of the applicationof local friction coecients in ways that are not yet quantitatively described.Additionally, to allow extension of the model to dierent geometries and multiplechannels, a general relation that predicts the reverse ow in all situations has tobe found rst, avoiding reliance on experimentally determined relations. At thispoint, therefore, the boundary of the a-periodical regime cannot be predictedby analytical means.

5.4 Results

Using the relations presented in section 5.2 to model the friction in the sys-tem and assuming a constant heat loss of 450W per channel, the model isimplemented in the Matlab environment. In gure 5.1, the simulated stabilityboundaries are displayed against the measured stability map. For the low inletfriction case, both predicted boundaries coincide with the measured ones quitewell. We can conclude that the assumptions were correct: The in-phase oscilla-tion is rst encountered when the coolant reaches the saturation temperature atthe top of the chimney and the boundary between the a-periodical and the out-of-phase oscillations are governed by achieving a geysering state at zero reverseow.

For the high inlet friction case, the predicted in-phase stability boundary alsocorresponds quite well with the experimental data. The out-of-phase bound-ary, however, is in the middle of the a-periodical region. The deviation from themeasurements is due to the fact that geysering/reverse ow-induced a-periodicaloscillations extend the a-periodical regime into the out-of-phase regime in thiscase. As we have already seen in section 4.1.3, this type of a-periodical behaviorhas previously been observed at high inlet friction conditions. Further inves-tigation of the experimental data around the predicted out-of-phase stabilityboundary, shows that it indeed marks the transition from ashing/geysering-induced a-periodical oscillations to geysering/reverse ow-induced a-periodicaloscillations. From this we can conclude that although the predicted boundarydoes not correspond with the boundary of the out-of-phase regime anymore, itstill correctly predicts the point at which geysering must occur.

Nevertheless, we must conclude that the condition that geysering must alwaysoccur is not enough to guarantee out-of-phase oscillation at high inlet friction.

57

0.5 1 1.5 2

0

2

4

6

8

10

12

14

16

18

20

Power/rod [kW]

Sub

cool

ing

[K]

Stable flowIn−phase osc.A−periodical osc.Out−of−phase osc.Higher order osc.Simulations

(a) Kin = 8, 9

0.5 1 1.5 20

5

10

15

20

25

30

35

40

45

50

Power/rod [kW]

Sub

cool

ing

[K]

Stable flowIn−phase osc.A−periodical osc.Out−of−phase osc.Higher order osc.Low subc. stable flowSimulations

(b) Kin = 370

Figure 5.1: The experimentally determined stability map for CIRCUS IV andthe prediction of the upper stability boundary and the out-of-phase oscillationboundary for a common inlet friction of (a) Kin = 8, 9 and (b) Kin = 370.

58

Figure 5.2: A schematic of two of the inlet channels between the core and thelower inlet plenum.

The correct transition to the out-of-phase regime can only be predicted oncea relation for the magnitude of the reverse ow has been found. For now, wewill treat this discrepancy as a boundary condition to the model. We have seenin section 4.1.3, that the out-of-phase regime is disturbed at the moment thereverse ow becomes large enough to pass through the lower inlet plenum andfeed hot coolant to the other channels. This is illustrated schematically in gure5.2. We can therefore expect the model to be correct if the distance covered bythe reverse ow, is smaller than the distance from the core of a channel to thelower inlet plenum. The condition becomes:

t2

t1

vrfdt

Linlet=

Lrf

Linlet≤ 1 (5.14)

Where vrf is the reverse ow speed in the channel and t1 and t2 the start andthe end of the reverse ow. Linlet is the length of the inlet channel between thelower inlet plenum and the core inlet, as indicated in gure 5.2.

In gure 5.3a, the modeled and experimentally determined stability boundariesfor the in-phase and out-of-phase oscillations in CIRCUS IV are plotted in thedimensionless Npch-Nsub plane. For the in-phase stability boundary, the experi-ments at higher phase change numbers seem to correspond well to the predictedvalues, but at lower values, the experiments deviate from the model. Due to thehigh relative uncertainty in the determination of the ow through the systemat low mass ows, it is hard to draw a conclusion from this information. Error

59

0 20 40 60 80 1000

20

40

60

80

100

120

Xe = 0

Npch

Nsu

bCIRCUS IV

Xe = 0X

e = 0X

e = 0X

e = 0

Model In−phase SBModel Out−of−phase SBExperiments In−phase SBExperiments Out−of−phase SB

(a)

0 20 40 60 80 100 1200

50

100

150

Xe = 0

Npch

Nsu

b

Xe = 0X

e = 0X

e = 0

Model CIRCUS IVExperiments CIRCUS IVModel CIRCUS IIExperiments CIRCUS IIModel CIRCUS IExperiments CIRCUS I

(b)

Figure 5.3: The predicted and measured stability in-phase and out-of-phasestability boundaries for the CIRCUS IV setup (a) and the in-phase stabilityboundaries for CIRCUS I - IV compared to experiments conducted by Manera[4] and Marcel [5].

60

bars have been added to show the extent of the uncertainty in the phase changenumber due to the uncertainty in the determination of the ow. Nevertheless, itseems that there is some eect at low mass ows that the model fails to predict.One eect that plays a role in these conditions, for example, is the additionaldriving head introduced by extracting heat from the coolant at the top of thefacility. The eect is negligible during normal operation, but it is shown to beable to drive a very small ow through the system when no power is applied tothe heating rods. It is believed by the author that this eect plays a large rolein the deviation from the predicted stability boundary.

For the determination of the phase change number for the out-of-phase sta-bility boundary data, the time-averaged minimum value for the primary massow is used, since the geysering oscillations are occurring from a steady singlephase ow circulation in each channel. Due to the strong uctuation of theminimum mass ow, the uncertainty in the determination of Npch is quite large(indicated by error bars in gure 5.3a). As with the upper stability boundary,the experimental data corresponds well to the predicted out-of-phase stabilityboundary.

Moreover, the predicted values for the in-phase stability boundaries of the pre-vious CIRCUS congurations also correspond well to the experiments, as can beseen in gure 5.3b. The experimental data from the CIRCUS I setup is shiftedtowards the right due to the relatively high power over ow as a result of thehigh common friction coecient applied during measurements, but the modelpredicts this behavior correctly. We can conclude from the results in gures 5.1and 5.3, that the driving head and the frictional pressure drop are indeed theterms that are most important for stability in the system and that the constantheat loss approximation is acceptable. The model approximates the stabilityboundaries for the in-phase and out-of phase regimes well enough to allow forextension to systems with larger numbers of parallel channels.

5.5 Extension to n channels

Now that we have veried the model against experimental data acquired overthe past years, we can continue to extend the model to geometries with moreparallel channels. For this extension of the model, we will keep all parametersrelated to the geometry of the setup (e.g. the localized frictional pressure dropsand the diameter of the downcomer) the same as in the CIRCUS IV setup.

In gure 5.4a the in-phase stability boundary is extended to a system with 8,16 and 64 channels. From the trends in the gure it can be concluded that thedivision into many separate channels has a destabilizing eect on the in-phasestability boundary for a system operating at a xed power. In-phase massow oscillations are already encountered at a much higher subcooling. In fact,the stability boundary seems to be quite sensitive to channel division. Sincethe peripheral geometry was kept the same during all simulations, it must beconcluded that the increased instability is due to wall friction added by channeldivision.

In the dimensionless Npch-Nsub plane, division of the core and chimney sectionsinto separate channels, causes the in-phase stability boundary to shift to the

61

(a) The predicted in-phase stability boundaries in the power-subcooling plane for multipleparallel channels in the CIRCUS IV geometry.

(b) The predicted in-phase stability boundaries in the dimensionless Npch-Nsub plane fordivision of the core and chimney cross-sectional area into n channels.

Figure 5.4

62

right, as can be seen in gure 5.4b. This is in accordance with the trendsdisplayed in the power-subcooling plane. For example, suppose we supply anequal, xed power and inlet temperature to two natural circulating systems thatare identical in any way except for the measure of channel division. The coreand chimney of system A is partitioned into eight separate channels, whereassystem B is tted with sixteen parallel channels. The operational point of thesefacilities has been indicated in gure 5.4a. It can be noticed from the system thatsystem A is stable at the indicated operational point and system B is unstable,since it is located below the predicted stability boundary for division in sixteenchannels. Due to less wall friction in system A, the induced mass ow throughthe system will be larger in that system. As a consequence, the operational pointof system A in the dimensionless plane will shift to the left with respect to theoperational point of system B, due to the inverse dependence of Npch on theow. This shift is indicated in gure 5.4b. We see that the predicted stabilityof the systems at the indicated operational points has not changed. This meansthat both results support the same conclusion: Division into separate channelshas a destabilizing eect on the system. In this plane, it can also be notedthat the unstable behavior increases quite rapidly with the number of separatechannels into which the core and chimney are divided: The 64 channel in-phasestability boundary has signicantly shifted to the right5.4b.

The trend of stability boundaries shifting towards the right and away from thechimney exit zero quality line in the dimensionless plane is also in concurrencewith the trend found in chapter 4 during the comparison of systems with anincreasing common inlet friction coecient (gure 4.15b). This accordance wasexpected, since the model predicts the stability boundary from a single phase,steady state situation. As a result, the location and origin (i.e. wall friction orlocal friction) of the friction in the system does not inuence the location of thestability boundary.

Since the model was also shown to apply for the out-of-phase boundary, we canexpect a similar shift towards the right of the dimensionless plane in combinationwith a diversion from the Xe = 0 line. In gures 5.5, both the in-phase and out-of phase stability boundaries have been plotted for dierent levels of channeldivision. Bear in mind that although the results in the dimensionless planeshould be applicable to all systems at the same operational point, condition 5.14has to be met for a correct prediction of the out-of-phase stability boundary. Ifnot, this means that a prediction was only made for the boundary below whichonly geysering events will be encountered. The actual behavior of the systemwill in that case most likely be a-periodical, as discussed in section 5.4.

From the gures it can be concluded that the out-of-phase stability boundaryindeed shows a similar trend as the in-phase stability boundary. Also, the out-of-phase boundary stays below the in-phase stability boundary in the CIRCUSIV operational range, which means that at increasing the inlet temperature froma stable circulation, in-phase oscillations will always be encountered before theoscillations become a-periodical. We can therefore conclude that for systemsat the same operational point in the Npch-Nsub plane, the system with largestchimney division will be most stable with respect to both in-phase and out-of-phase behavior.

63

Figure 5.5: An overview of the in-phase and out-of-phase stability boundaries(SB) for dierent measures of channel division.

64

Chapter 6

Parameter study

In the previous chapters we have studied the stability behavior in systems withparallel channels. We must however not forget, that we are still dealing witha nuclear reactor. Some of the boundary conditions that have been used whilestudying the stability behavior of the multi-channel systems might not be re-alistic in a real reactor. One of these is the power prole. So far, we haveassumed that power is applied to each channel equally. In the ESBWR, or anyother Boiling Water Reactor, such a at power prole is not realistic due to thegeometry of the reactor. This means that the applied power will depend on thelocation in the reactor. The eects of such a power skew on the stability of theparallel channel natural circulation BWR is the topic of the rst part of thischapter. In the second part of the chapter, a proposed method to compensatefor the eects of a power skew by applying localized friction to the inlets of theseparate channels is investigated. Finally, in the last section of this chapter, theimplications of the acquired results to ESBWR stability will be discussed.

6.1 Power skew

To simulate the eects of a power skew in the CIRCUS facility, a 10% and 20%higher power (Ptop) is applied to one of the heated channels with respect tothe other three (Plow). The average power per rod applied to the system cantherefore be designated Pavg = 1

4Ptop + 34Plow. Friction coecients and all other

parameters are kept at the same values as during the low inlet friction stabilityexperiments in chapter 4.

6.1.1 Stability eects

We can see in gures 6.1a and 6.1b that imposing a power skew has a signicanteect on the occurrence of the dierent instability phenomena in the setup. Thesize and arrangement of the instability regimes in the power-subcooling planedeviates from the equal-power situation displayed in gure 4.10a (indicated bythe dashed lines in gures 6.1) and continue to change with increasing power

65

skew. The most interesting observation, is that the position of the upper sta-bility boundary moves upward in the power-subcooling plane. This means thefacility as a whole becomes less stable at the same applied power.

The increased instability can be explained by the fact that, as we have claimedin chapter 5, the setup rst becomes unstable at the moment the coolant reachesthe saturation temperature at the top of the chimney. Theoretically, the channeloperating at Ptop will reach this point at higher subcooling than a system withfour channels all equally operating at Pavg. The fact that three other channelsin the power skew have not become unstable yet, does not change the fact thatthe facility as a whole displays unstable behavior, hence the upward movementof the stability boundary in the power-subcooling plane.

The eect of the power skew becomes even more interesting when we comparethe upper stability boundary in another way. In gure 6.2 the measured stabilityboundary at a at power prole is indicated by the dashed line. Subsequently,the upper stability boundary at 20% power skew is compared to this line in twodierent ways. The red line indicates the stability line determined on the basisof Pavg, as was done in gure 6.1. The blue line, however, indicates the samestability line determined on the basis of Ptop. Comparing the at power proleand 20% power skew situation in the latter way, means that we are comparingthe stability boundary of the power skew to the stability boundary of a atpower prole in which Ptop is applied to each rod.

From gure 6.2, we can conclude that the upper stability boundary during apower skew in which the maximum power is Ptop, does not deviate much fromthat of a at power prole that is completely at Ptop.We can therefore concludethat the stability of the system as a whole is approximately governed by thechannel to which the highest power is applied. This is an interesting result formulti-channel natural circulation reactors. The small increase in stability wedo notice in gure 6.2, is thought to be due to the fact the the four chimneysare combined into a single channel at the top of the chimney. This meanssome mixing will occur between the relatively hot coolant from the high-powerchannel and the colder coolant from the other channels, causing the power skewsituation to be slightly more stable than the reference at power prole at Ptop.

Since the mass ow has not signicantly changed during the application of thepower skew, we see the same trends in the dimensionless plane. This is shownin appendix D.

6.1.2 Shifting stability regimes

In addition to the deviation of the upper stability boundary, the location ofthe instability regimes in the power-subcooling plane diers signicantly. Ingures 6.1a and 6.1b, it can immediately be seen that the in-phase oscillationregime becomes larger at increasing power skew, not only due to the upwardshift of the upper stability boundary, but also by extending downward in thepower-subcooling plane. Apparently, in-phase oscillations are sustained for alarger range of power and inlet temperature conditions. It is expected thatthis is due to the fact that the reverse ow in channel 1, induced by geyseringevents in channels 1-3, is smaller. This is shown schematically in table 6.1. As a

66

(a)

(b)

Figure 6.1: The stability map for a situation with a 10% higher power (a) anda 20% higher power (b) in channel 1 as a function of Pavg. The dashed linesindicated in the gure represent the stability boundaries for a at power prole.

67

P [kW]

Sub

cool

ing

[K]

0.5 1 1.5 20

2

4

6

8

10

12

14

16

18

20 No Power skew20% Power skew P=average power/rod20% Power skew P=Ptop

Figure 6.2: The in-phase stability boundary for a at power prole comparedto the in-phase stability boundary in a 20% power skew situation. For the samemeasurement, the power skew stability boundary is displayed as a function ofPtop and as a function of Pavg.

t1 t2 t3 t4

Ch.1 F ↓ F ↓

Ch.2 ↓ G ↓ GCh.3 ↓ G ↓ GCh.4 ↓ G ↓ G

Table 6.1: In-phase oscillation during a power skew: The induced reverse owin channel 1 is smaller than would be the case with a at power prole at equaltotal power. The intervals between the events are not constant.

consequence, it takes a lower subcooling to induce a secondary geysering eventin channel 1. This way, the cascade of geysering events leading to a-periodicalbehavior is prevented.

We also notice that the a-periodical regime is moving downwards with increas-ing power skew. The a-periodical oscillations at low subcooling were found to besimilar to those described as geysering/reverse ow-induced a-periodical oscilla-tions in section 4.1.3. It is found that the average reverse ow in the low-powerchannels is higher than in the channel operating at Ptop and also higher thanthe reverse ow in a at power prole at Pavg. As a result, hot coolant can bebrought into the lower inlet plenum, facilitating the occurrence of this type ofa-periodical behavior. At high power, the reverse ow even becomes so dom-inant that the out-of-phase regime is not encountered at all: the a-periodicalregime borders the higher order out-of-phase regime.

The upward shift of the higher order out-of-phase regime itself is interesting too.

68

We have seen in chapter 4, that these oscillations are driven by geysering andreverse ow. In addition, the oscillations are usually asymmetrical in the sensethat only reverse ow is encountered in some channels, whereas only geysering isencountered in the other channels. The combination of the increased reverse owin the low-power channels and the asymmetry of the power skew, can thereforebe expected to facilitate higher order out-of-phase oscillations at much highersubcooling.

Even more interesting, is that the low subcooling stable ow regime is encoun-tered in the 20% power skew situation. Apparently, the low subcooling stabilityboundary moves upwards considerably. Considering that the upper stabilityboundary has not moved that much in the power-subcooling plane, the to-tal unstable regime between the two boundaries is signicantly decreased. Inchapter 4, we already noticed that there were, in fact, two dierent stabilityboundaries associated with low subcooling stable ow: an initiation boundaryand a maintenance boundary. The detection of the low subcooling stable regimein a power skew situation can be explained by the fact that the initiation of theinter-channel circulation associated with low subcooling stable ow, can occurat much higher subcooling. This is made clear in gure 6.3. Starting from pointA, where the system is in the higher order out-of-phase regime, we slowly de-crease the inlet subcooling. At point C, we would encounter the low subcoolingstable ow in a setup with a at power prole. Point C is therefore called theinitiation boundary. At this point, the coolant would start to partly recirculatebetween channels, as explained in section 4.1.6. If we increase the subcoolingagain, the system returns to the higher order out-of-phase regime in point D,which is therefore called the maintenance boundary. Due to the applicationof a power skew and the resulting asymmetry between the channels, the inter-channel recirculation, and therefore the low subcooling stable regime, is alreadyinitiated at point B. If we subsequently reduce the inlet temperature again, thelow subcooling stable regime can again only be maintained until we arrive atpoint D.

We can conclude from this that by applying a power skew, the separation be-tween the initiation boundary and the maintenance boundary in the power-subcooling plane is decreased. It is expected that this eect becomes evenstronger for larger power skews, since these would increase the asymmetry ofthe induced reverse ow in the system. For multi-channel systems in whichpower skews are encountered, this means that it is useful to investigate the ex-act location of the maintenance boundary in the power-subcooling plane, sinceit determines when the regime can occur in contrast to the initiation boundary,which only indicates when it must occur.

6.1.3 Time dependent behavior

All instabilities encountered during power skew measurements can be clearlyclassied into one of the six regimes described in chapter 4, with one notableexception. When the system rst becomes unstable at high subcooling, weencounter a previously unobserved type of oscillation. In gure 6.4, the totaland partial mass ow characteristics of such an instability is shown. We see that,logically, the high-power channel (channel 1) shows a ashing-induced instability

69

Figure 6.3: A schematic representation of the dierent boundaries involved withlow subcooling stable ow. Point D is moved somewhat to the right for clarity;in the example the power is the same for all points.

t1 t2 t3

Ch.1 F ↓ ↓Ch.2 ↓ F ↓Ch.3 ↓ ↓ GCh.4 ↓ ↓ G

Table 6.2: Flashing induced oscillation at conditions just below the stabilityboundary in the power-subcooling plane (at Ptop = 2, 2 kW (channel 1), Plow =2, 0kW and Tsub = 17, 3K). t1 and t2 are separated in time by approximately 20seconds, t3 follows t2 within seconds.

rst. After that, nothing happens for almost 20 s, before the other three channelsdisplay in-phase oscillation. The interesting thing is that even at power and inlettemperature conditions just below the stability boundary, ashing events do notonly occur in the high-power channel. Apparently, ashing induced instabilitiesalso occur in the low-power channels, at conditions in which they would notoccur in a at power prole. It is believed that this is due to a slightly lowermass ow in the low-power channels, but this cannot be experimentally verieddue to the high relative uncertainty in the dierential pressure drop sensors atthese conditions. The oscillation timetable is indicated in gure 6.2.

Although the oscillation has two distinct frequencies, it is a ashing-induced,periodically recurring oscillation and is therefore ranged with the in-phase os-cillations in the gures in this chapter.

6.2 Inlet friction distribution

It is expected that some of the stability eects of a power skew can be compen-sated by adjusting the inlet friction to each channel separately. By increasing

70

(a) (b)

Figure 6.4: The partial (a) and total (b) mass ow of the instability at Ptop = 2, 2kW (channel 1), Plow = 2, 0kW and Tsub = 17, 3K.

or decreasing the friction component by means of valves, it will be possible togovern the ow through each channel and with that the heat transferred to thecoolant per unit of mass. To experimentally test the eect of imposing an inletfriction to a single channel, we will return to the at power prole and increasethe inlet friction coecient of channel 1 to Kin,ch1 = 7, 4. The inlet frictioncoecients of the other channels will be kept at their standard values (see table3.2). The resulting stability map is shown in gure 6.5.

At a rst glance, we see the same eects as with the application of a power skew.The system as a whole has become just slightly less stable for a system at a xedpower, while at the same time the in-phase regime is extended downwards inthe power-subcooling plane. There are also signicant dierences however. Forexample, we see that the out-of-phase and higher order out-of-phase regimes areat the same locations as at equal (low) channel inlet friction, whereas an upwardshift was found during power skew experiments. Additionally, when we have alook at the movement of the upper stability boundary in the dimensionless planein gure 6.6, we see that the increased friction coecient has a slight stabilizingeect for systems at the same operational point. This result is in accordancewith our conclusion about the inuence of friction on stability in the previouschapters.

There is another important dierence between the power skew and the frictiondistribution situations. We have seen that in the former case, ashing-inducedevents occur in each of the four channels, also at power and inlet conditions atwhich these phenomena would not occur in a at power prole at Plow. This isnot the case with the applied friction distribution. Although instabilities for thesame system occur at higher subcooling, the instabilities are much less violent.This is due to the fact that at conditions just below the stability boundaryonly the channel to which the additional friction is applied, shows ashing-induced instabilities, even where these instabilities normally would occur in theother channels at equal friction distribution. A schematic representation of theinstability is presented in table 6.3. This eect is almost certainly due to higherows in channels 2, 3 and 4 (after all, at almost the same driving head, partlyclosing o one channel would force a larger ow in the other channels), but

71

Applied power per rod [kW]

Sub

cool

ing

[K]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

6

8

10

12

14

16

18

20 Higher order osc.Out−of−phase osc.A−periodical osc.In−phase osc.Stable flow

Equal friction SBs

Figure 6.5: The stability map for a situation with a raised inlet friction coef-cient in channel 1: Kinlet(ch1) = 7, 4 and Kinlet(ch2 − 4) ≈ 3, 4 (see table3.2). The dashed lines indicate the stability boundaries in case of equal frictiondistribution.

0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

80

90

100

110

Xe = 0

Npch

Nsu

b

No friction distributionFriction distribution K(in,ch1)=7,4

Figure 6.6: The upper stability boundary in case of an enlarged local frictionin channel 1 (Kin,ch.1 = 7, 4), compared to the case with equal distribution offriction coecients (Kin,ch ≈ 3, 4), see table 3.2.

72

t1 t2 t3

Ch.1 F F FCh.2 ↓ ↓ ↓Ch.3 ↓ ↓ ↓Ch.4 ↓ ↓ ↓

Table 6.3: The schematic representation of the instabilities just below the upperstability boundary in case of an inlet friction distribution. The consecutiveevents are separated by long time intervals.

as before, this could not be experimentally conrmed due to the high relativeuncertainty in the dierential pressure signal at these conditions.

We can conclude from this that a power skew increases the range of conditions inwhich ashing-induced instabilities can occur in the low-power channels, whilechannel inlet friction reduces this range for the low-friction channels. It cantherefore be expected that the application of additional local friction to thelow-power channels in a skewed power prole, will limit the occurrence of ash-ing induced instabilities in the high-power channels. At the same time, theoccurrence of these instabilities is increased in the channels to which the fric-tion is applied. As a result, the heat transferred to the coolant per unit mass canbe equalized over all channels. It would be interesting to investigate if such acombined power and friction skew, would cause the system as a whole to becomemore stable or less stable.

6.3 Implications for the ESBWR

Returning to the ESBWR itself, we can draw two main implications from theresults in the last two sections:

1. One of the most important results is that it was found that a power skewhas a destabilizing eect. The thermal hydraulic stability of the systemis governed by the channel to which the highest power is applied. Thiseect has to be taken into account during the startup of the reactor ifashing induced instabilities are to be avoided. In the ESBWR, this eectis expected to be damped by two eects. First of all, the separate channelsin the ESBWR are combined into a common riser at a certain height. Thismeans that mixing of the relatively hot coolant and the colder coolant fromdierent channels can be expected, before the coolant reaches the top ofthe reactor, where the lowest saturation temperature will be encountered.Secondly, due to the large number of channels in the ESBWR, a smallnumber of high-power channels will probably not have a large inuenceon the mass ow nor on the occurrence of ashing induced phenomena inthe other channels. It becomes a completely dierent situation, however,when there is a cluster of high-power channels. Such a situation couldconsiderably increase the amount of ashing-induced instabilities in theother channels and have a large inuence on the mass ow through thesystem, thus making the whole system less stable.

73

2. Secondly, we have found that raising the channel inlet friction coecientsslightly destabilizes systems at the same, xed, power, but has a stabiliz-ing eect for systems at the same operational point. It is expected thatincorporating higher local friction coecients to low-power channels in thedesign of the reactor can be utilized to even the heat transferred to thecoolant per unit mass over the channels.

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Chapter 7

Conclusion and

Recommendations

7.1 The CIRCUS IV facility

As a result of this project, the CIRCUS IV facility is now fully calibrated andadjusted to allow easier comparison with its predecessors. Many adjustmentshave been made to the setup: insulation was applied, the thermocouple posi-tions were equalized and the measurement and control of the inlet temperaturehas been improved signicantly. Among the most notable improvements is theinstallation and implementation of an array of cheap and easy to use opticalvoid sensors. These sensors have shown their value in determining the pro-duction of vapor over the complete length of the chimneys at high frequency.In addition to this, the detection of dierent ow regimes in the facility basedon the photodiode signal was shown to be possible. Bubbly ow and in someconditions slug ow, have been seen to produce recognizable signals that werecross-checked with high-speed camera images.

It is believed that the detection of the void regimes can be extended to a pointwhere it is possible to determine the ow regimes throughout the length of thechimney during ashing or geysering events. Besides being very useful to numer-ical simulation of the time-dependent phenomena in CIRCUS, the informationcould also provide more understanding of the dynamic processes during owinstabilities and the comparability of dierent setups. On this topic a bachelorproject was formulated and started.

7.2 Instability phenomena

The instability phenomena occurring in a setup with four parallel channels hasbeen investigated in detail. In total, six dierent stability regimes have beenfound. Five of these have been shown to be similar to the previously foundinstability regimes in CIRCUS II. Additionally, the higher order out-of-phase

75

regime has been identied as a separate regime. The oscillations in this regimeoften include one or more channels that only show reverse ow. Since theexistence of some of the higher order oscillations is clearly linked to the fact thatthe system has more than two channels, it is expected that more complicatedoscillations will arise in systems with even more parallel channels.

It was also found that the behavior in all encountered instability regimes can beexplained by a combination of three instability phenomena: ashing, geyseringand reverse ow. During in-phase oscillations, all three of these phenomenaplay a role, whereas out-of-phase oscillations and higher order out-of-phase os-cillations are only caused by geysering and reverse ow. In the a-periodicalregime, two distinguishable instability mechanisms have been found, a ash-ing/geysering/reverse ow-induced and a geysering/reverse ow-induced regime.The latter of these a-periodical oscillations only occurs in situations with highreverse ow. The low subcooling stable regime was found to be a combinationof continuous ashing in two channels, combined with continuous reverse owin the other two. Due to the internal circulation in this regime, a hysteresiseect is encountered: more energy needs to be applied to the system to attainthis regime than to maintain it. As a result, both a maintenance and an initi-ation boundary were detected for this regime. It was also found that the lowsubcooling stable regime could be initiated above the initiation boundary, byapplying a perturbation in the form of a power skew or a friction distributionover the channels.

It is expected that detailed study of the higher order out-of-phase regime couldresult in the determination of another separate regime: the 1 vs 1 vs 1 vs 1 gey-sering regime. In this case each channel shows a separate geysering instability atequal time intervals. So far, the behavior has been classied with the the higherorder regime, but some experiments seem to indicate that there is a xed regionin the power-subcooling plane where 1 vs 1 vs 1 vs 1 oscillations can be observed.Additionally, it is believed to be of interest for many-channel natural circula-tion systems, to study the pairing of channels during out-of-phase oscillations.At the moment, the process of the two-by-two ordering of geysering channelsin this regime is not yet fully understood. If conditions in which out-of-phaseoscillations were ever encountered in a reactor, the number of paired channelscould have a large inuence of the magnitude of the mass ow oscillation.

Finally, it was shown that the in-phase stability boundary for CIRCUS IV islocated below the zero quality at the chimney exit line. This means that vaporcan be produced during high subcooling stable circulation. This result is inaccordance with ndings by Manera and Marcel. Furthermore, it was shown bythe comparison of the experimentally determined stability boundaries that theunstable operational regime for CIRCUS IV is larger than that of CIRCUS I andII in the dimensionless Npch −Nsub plane for high phase change numbers. Forlower phasechange numbers, however, CIRCUS IV is more stable. In addition,it was shown that for increasing values of the common inlet friction, the in-phasestability boundary in the dimensionless plane deviates from the zero quality atthe chimney exit line, thus increasing the high subcooling stable ow regime.This also means that systems with high common inlet friction are more stableat the same operational point than systems with low common inlet friction.

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7.3 Theoretical model and simulation

A simple analytical model was composed to estimate the boundaries of the in-phase and out-of-phase oscillation regimes for natural circulation systems withparallel channels. The model is based on a steady state approximation and theassumption of constant heat loss from the channels. The predictions made bythe model, were shown to correspond well to the experimentally determined in-phase and out-of-phase stability boundaries in CIRCUS I, II and IV. Extensionof the model to multiple channels, showed that the in-phase and out-of-phasestability boundaries are quite sensitive to channel division. Since they are basedon similar assumptions, both boundaries display the same shifts in the power-subcooling and Npch-Nsub plane under channel division. It can be concludedfrom the predictions made by the model, that the overall stability of systems atthe same operational point is increased with the amount of chimney division. Asystem operated at xed power and inlet temperature conditions, however, ex-periences a decreased stability at chimney division. For the ESBWR this meansthat if the same stability characteristics are to be maintained with a dividedchimney during startup of the reactor, the power or the inlet temperature hasto be reduced.

It is believed that the boundaries of the a-periodical regime and even the higherorder out-of-phase and low subcooling stable ow regimes can be predicted basedon similar, simple assumptions, when reverse ow is more fully understood andcan be modelled for dierent geometries. The reverse ow is expected to bemainly determined by the values of the local common inlet and chimney exitfriction coecients. A further study into the inuence of these frictions on themagnitude of the reverse ow might therefore deliver an approximate relationthat can be applied in extending the simple analytical model.

In addition, it is expected that the analytical model can be improved by ap-plying more realistic relations for the heat loss to the surroundings. For theestimation of the stability boundaries, this is not believed to be a signicantimprovement, but it may shed light on the proportion of the heat loss in thesystem in comparison to the heat lost in vaporization processes. If the heatloss is relatively large, this could signicantly reduce the high subcooling stableregime below the zero quality at the chimney exit line in well insulated reactorsand therefore have important consequences for the startup procedure of naturalcirculation BWRs.

Much eort was also put into the adaptation of a numerical model, created byMarcel [5] for CIRCUS I, to the CIRCUS IV setup. Although this model, inthe form it was presented, delivers good results for the single chimney setup,its absence of wall friction terms and the denition of the nodal model, compli-cate its extension to multiple parallel channels. Furthermore, predictions basedon an extension of the model to multiple channels, using similar assumptionsas in the simple analytical model used in this thesis, do not correspond withexperimental data. It is believed by the author that a broad revision of thismodel is necessary to be able to apply it to systems of parallel channels as en-countered in the ESBWR. It is believed that this model, or a model based onthe same method, could be applied to CIRCUS IV successfully in the courseof one complete Master's Project or as a part of a PhD research. It would be

77

especially interesting if the results of such a model were to be combined with thesimple analytical model described in Chapter 5. Integrated, they could providea means to predict most of the boundaries between the stability regimes.

7.4 Power skews

Since the power prole in the ESBWR will not be a at prole, the eect of theapplication of a power skew was investigated by applying a higher power to oneof the heating rods in CIRCUS IV. It was shown that a power skew destabilizesthe system and that the in-phase stability boundary in the power-subcoolingplane is governed by the channel to which the highest power is applied. Thepower skew is shown to not only increase the conditions under which ashing-induced phenomena can occur in the high-power channel, but also in the low-power channels. As a result, the amplitude of the mass ow oscillations is notonly governed by the high-power channels.

It was also found that due to a signicant power skew, the initiation boundaryfor low subcooling stable ow is encountered at much higher subcooling. It canbe concluded that information about the location of the maintenance boundaryfor low subcooling stable ow is more useful for ESBWR operation than thedetermination of the initiation boundary. It might therefore be interesting toinvestigate the location of the maintenance boundary in the power-subcoolingplane and the dimensionless plane in the future.

Furthermore, it was shown that the application of additional local friction toone of the channels, has a stabilizing eect on the system. Also, such a localfriction limits the occurrence of ashing-induced instabilities in the remaining,low-friction channels. This nding implies that the dierences in the power overmass ow ratio can be equalized over all channels by incorporating channel inletfrictions in the ESBWR. These local frictions should in that case be situated inthe low-power channels in the reactor.

It is speculated that a combined power and friction skew has a stabilizing eecton the reactor in the dimensionless Npch-Nsub plane as a result of the additionalfriction added to the system and as a result of equalizing the heat transferper unit mass over the channels. It may be interesting to research dierentcongurations of power skews and inlet frictions to determine this eect, forexample in the course of a Bachelor's project.

78

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80

Acknowlegdements

I would like to thank Dick de Haas for his patience and enthusiasm in explainingthe details of the operation of the CIRCUS IV facility and answering my manyquestions about the data acquisition and previous setups. In particular, I wouldlike to thank him for personally spot-welding the physical connections for controland data acquisition between the void sensors, power supply and DAQ system.

Also, I would like to thank August Winkelman. He has been helpful in manyways, but especially in coming up with the best method to apply the idea ofoptical void sensors.

Furthermore, I would like to extend gratitude to Christian Marcel for sendingme his model for further study and Annalisa Manera for her helpful attitudeand excellent documentation of CIRCUS I data.

Last, but not least, I would like to thank Martin Rohde for his help throughoutthe project, the thorough feedback on the report and sharing general enthusiasmover new ndings. Martin, I'm gonna have to need you to keep up the goodwork, that would be greeaat. **

81

Nomenclature

Nomenclature

A Area [m2]D Diameter [m]Ff Frictional force [N ]f friction coecientg Gravitational acceleration [ms2 ]h Heat transfer coecient [ W

m2K ]hl Liquid enthalpy [ J

kg ]

K Local Friction factor [-]Kin Common inlet friction factor [-]L Length [m]l Interval length [m]

M Mass ow [kgs ]

Npch Phase change number [-]Nsub Subcooling number [-]P Power [W ]p pressure [Pa]q Heat transfer [W ]qloss Heat loss from the channels [W ]R Radius [m]Re Reynolds number [-]T Temperature [°C]t time [s]u velocity vector [ms ]v velocity [ms ]

Greek symbols

α Void fraction [-]δ Small perturbationε Relative roughness [m]λ Heat conductivity [ W

mK ]φ′′ Heat ux [ W

m2 ]χ Quality [-]

ρ Density [ kgm3 ]

τ Time delay [s]

82

Superscripts and subscripts

avg Averagec Corech Channelci Core inletdc Downcomerfg Dierence between (saturated) vapor and liquid propertiesl liquidlow Lowest power in power skewpch phase changere Riser exit = Chimney exitrf Reverse owsat saturationsub Subcoolingtop Highest power in power skewup Upward (ow)v vapor

83

List of Tables

2.1 Maximum core damage frequencies for several Boiling Water Re-actor designs and two modern Pressurized Water Reactor designs:The AP1000 and the European Pressurized Reactors. [6]. . . . . 17

3.1 Relevant characteristics of the dierent CIRCUS congurations. . 20

3.2 The friction coecients related to the valves and bends in theinlet channels below the core. . . . . . . . . . . . . . . . . . . . . 22

4.1 An example of a timetable used to describe the instabilities oc-curring in the setup. . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2 The events timetable for in-phase oscillations. Event t2 followsevent t1 within seconds. The time span between t2 and t3 is verylong. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3 An example of a timetable for behavior in the a-periodical regime.It must be emphasized that the events are not equally separatedin time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.4 High reverse ow a-periodical behavior timetable. . . . . . . . . 34

4.5 The oscillation timetable for out-of-phase oscillations. In thiscase, the events are equally separated in time. . . . . . . . . . . . 36

4.6 The channel pairing process for out-of-phase oscillation, as sug-gested by the author. Events t1 and t2 occur at practically thesame time, while the time spans between t2, t3, t4 and t5 are larger. 36

4.7 Oscillation timetables for some of the higher order out-of-phaseoscillations. In all cases the interval between consecutive eventsis equal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1 Measured and calculated friction coecients in the CIRCUS IVsetup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.1 In-phase oscillation during a power skew: The induced reverseow in channel 1 is smaller than would be the case with a atpower prole at equal total power. The intervals between theevents are not constant. . . . . . . . . . . . . . . . . . . . . . . . 68

84

6.2 Flashing induced oscillation at conditions just below the stabil-ity boundary in the power-subcooling plane (at Ptop = 2, 2 kW(channel 1), Plow = 2, 0kW and Tsub = 17, 3K). t1 and t2 are sep-arated in time by approximately 20 seconds, t3 follows t2 withinseconds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 The schematic representation of the instabilities just below theupper stability boundary in case of an inlet friction distribution.The consecutive events are separated by long time intervals. . . 73

85

List of Figures

1.1 Schematics of Boiling Water Reactor vessels of dierent gener-ations. A typical BWR vessel (a) and the ABWR (b) and theESBWR (c) reactor vessels. . . . . . . . . . . . . . . . . . . . . . 5

1.2 The saturation temperature as a function of the pressure (a) andthe void fraction as a function of the ow quality for dierentsystem pressures (b). . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Temperature proles in the reactor vessel at dient conditions.The dashed line indicated the saturation temperature as a func-tion of height. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1 The historic and projected development of the world's population(a) and the total and projected world total energy consumption(b). Sources: UN department of economic and social aairs [9],EIA [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 The historical and future CO2 emissions as predicted by the Car-bon Mitigation Initiative (a) and a magnication of the stabiliza-tion triangle (b). Source CMI[12]. . . . . . . . . . . . . . . . . . . 12

2.3 CO2 emissions from traditional means of energy supply. Source:IAEA [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 The share of nuclear power in produced electrical energy world-wide (percentage). Source: IEA [10] . . . . . . . . . . . . . . . . 13

2.5 A breakdown of the typical buildup of the nuclear electricity gen-eration cost [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.6 The increasing simplicity of the Boiling Water Reactor Design. . 16

3.1 The total cross-sectional area of the chimney sections in the dif-ferent CIRCUS congurations, viewed from the top. . . . . . . . 19

3.2 A schematic version of the CIRCUS experimental setup. . . . . 21

3.3 One void sensors attached to the set-up (top view). . . . . . . . . 23

3.4 A set of pictures of the array of void sensors attached to theCIRCUS IV set-up. . . . . . . . . . . . . . . . . . . . . . . . . . . 24

86

3.5 Void sensor data (top) and the temperature at the chimney outlet(centre) after starting up the Circus IV facility at full power (11kW), as well as magnications of the void sensor signal for theindicated domains (bottom). . . . . . . . . . . . . . . . . . . . . 24

4.1 The primary mass ow signal in dierent stability regimes atP = 2200W/rod and Kin = 8, 9. The low subcooling stable owboundary is estimated. . . . . . . . . . . . . . . . . . . . . . . . 28

4.2 The total mass ow (a) and the channel temperature prole (b)as a function of time (0 - 100 s) during high subcooling stablecirulation at P = 1400W/rod, Tsub,exit = 15 K and Kin = 8, 9. . 29

4.3 The total mass ow and the partial mass ow per channel (a), thetemperature proles (b) and void detection data (c) as a functionof time for in-phase oscillation at P = 1, 4kW, Tsub,exit = 7, 3°CandKin = 8, 9. The time is indicated in seconds on the horizontalaxes (10 - 100) and on the vertical axes the axial position ofthe sensor in question is given. This has been claried by theschematic versions of the CIRCUS IV facility next to the pictures.Note that the temperature sensors are installed installed overthe whole length of the setup, whereas the void sensors are onlypresent in the chimney. From left to right, the images representthe channels 1 to 4, respectively. . . . . . . . . . . . . . . . . . . 31

4.4 The Total mass ow and the partial mass ow per channel (a),the temperature proles (b) and void detection data (c) for a-periodical oscillation at P = 1, 4kW, Tsub,exit = 5°C and Kin =8, 9. The time is indicated in seconds on the horizontal axes (10- 100) and on the vertical axes the axial position of the sensorin question is given. This has been claried by the schematicversions of the CIRCUS IV facility next to the pictures. Notethat the temperature sensors are installed installed over the wholelength of the setup, whereas the void sensors are only present inthe chimney. From left to right, the images represent the channels1 to 4, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.5 The Power Spectral Densities of a mass ow signal from the a-periodical regime (a) and from the out-of-phase regime (b). . . . 34

4.6 The Total mass ow and the partial mass ow per channel (a),the temperature proles (b) and void detection data (c) for out-of-phase oscillation at P = 1, 4kW, Tsub,exit = 0, 6°C and Kin =8, 9. The time is indicated in seconds on the horizontal axes (0- 70) and on the vertical axes the axial position of the sensorin question is given. This has been claried by the schematicversions of the CIRCUS IV facility next to the pictures. Notethat the temperature sensors are installed over the whole lengthof the setup, whereas the void sensors are only present in thechimney. From left to right, the images represent the channels 1to 4, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

87

4.7 The Total mass ow and the partial mass ow per channel (a),the temperature proles (b) and void detection data (c) for 2 vs.2 reverse higher order out-of-phase oscillation at P = 2, 2kW,Tsub,exit = 0°C and Kin = 8, 9. The time is indicated in secondson the horizontal axes (0 - 60) and on the vertical axes the axialposition of the sensor in question is given. This has been clariedby the schematic versions of the CIRCUS IV facility next to thepictures. Note that the temperature sensors are installed overthe whole length of the setup, whereas the void sensors are onlypresent in the chimney. From left to right, the images representthe channels 1 to 4, respectively. . . . . . . . . . . . . . . . . . . 38

4.8 The Total mass ow and the partial mass ow per channel (a),the temperature proles (b) and void detection data (c) for lowsubcooling stable ow at P = 1, 8kW, Tsub,exit = 1, 2°C andKin = 370. The time is indicated in seconds on the horizontalaxes (0 - 100) and on the vertical axes the axial position of the sen-sor in question is given. This has been claried by the schematicversions of the CIRCUS IV facility next to the pictures. Notethat the temperature sensors are installed over the whole lengthof the setup, whereas the void sensors are only present in thechimney. From left to right, the images represent the channels 1to 4, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.9 The concept of hysteresis in CIRCUS IV. . . . . . . . . . . . . . 41

4.10 The stability maps: (In)stability behavior in the power-subcoolingplane for Kin = 8, 9 (a) and Kin = 370 (b). Subcooling has beentaken relative to conditions at the chimney outlet. The verticalaxes in these images are not at the same scale. . . . . . . . . . . 43

4.11 The reverse ow relative to the upward ow in geysering channelsfor high and low inlet frictions. . . . . . . . . . . . . . . . . . . . 44

4.12 The average ow in the stable ow regimes for varying buer levelheights at P = 1, 4kW and Kin = 8, 9. . . . . . . . . . . . . . . . 45

4.13 The correlation of recorded signals from the void detection (thedriving force) and the corresponding mass ow in channel 1 dur-ing in-phase oscillation at P = 1400W and Tsub = 9, 5. . . . . . . 47

4.14 The stability maps for the dierent CIRCUS congurations. Sources:Manera [4], Marcel [5]. The vertical axes in the gures dier inscale. The respective stability lines have been drawn by the re-spective authors themselves. . . . . . . . . . . . . . . . . . . . . 48

4.15 Stability boundaries for the dierent CIRCUS congurations inthe Npch-Nsub plane. . . . . . . . . . . . . . . . . . . . . . . . . 50

5.1 The experimentally determined stability map for CIRCUS IVand the prediction of the upper stability boundary and the out-of-phase oscillation boundary for a common inlet friction of (a)Kin = 8, 9 and (b) Kin = 370. . . . . . . . . . . . . . . . . . . . . 58

88

5.2 A schematic of two of the inlet channels between the core andthe lower inlet plenum. . . . . . . . . . . . . . . . . . . . . . . . . 59

5.3 The predicted and measured stability in-phase and out-of-phasestability boundaries for the CIRCUS IV setup (a) and the in-phase stability boundaries for CIRCUS I - IV compared to ex-periments conducted by Manera [4] and Marcel [5]. . . . . . . . . 60

5.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.5 An overview of the in-phase and out-of-phase stability boundaries(SB) for dierent measures of channel division. . . . . . . . . . . 64

6.1 The stability map for a situation with a 10% higher power (a)and a 20% higher power (b) in channel 1 as a function of Pavg.The dashed lines indicated in the gure represent the stabilityboundaries for a at power prole. . . . . . . . . . . . . . . . . . 67

6.2 The in-phase stability boundary for a at power prole comparedto the in-phase stability boundary in a 20% power skew situation.For the same measurement, the power skew stability boundary isdisplayed as a function of Ptop and as a function of Pavg. . . . . . 68

6.3 A schematic representation of the dierent boundaries involvedwith low subcooling stable ow. Point D is moved somewhat tothe right for clarity; in the example the power is the same for allpoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.4 The partial (a) and total (b) mass ow of the instability at Ptop =2, 2 kW (channel 1), Plow = 2, 0kW and Tsub = 17, 3K. . . . . . . 71

6.5 The stability map for a situation with a raised inlet friction coef-cient in channel 1: Kinlet(ch1) = 7, 4 and Kinlet(ch2− 4) ≈ 3, 4(see table 3.2). The dashed lines indicate the stability boundariesin case of equal friction distribution. . . . . . . . . . . . . . . . . 72

6.6 The upper stability boundary in case of an enlarged local frictionin channel 1 (Kin,ch.1 = 7, 4), compared to the case with equaldistribution of friction coecients (Kin,ch ≈ 3, 4), see table 3.2. . 72

B.1 Thermocouple signals, including the PT100 signals during coolingdown of the CIRCUS facility before (left) and after calibration(right). The two images at the bottom are magnications ofthe respective upper curves. It can clearly be seen that aftercalibration the signals are within 0,5 K of each other. . . . . . . . 91

D.1 The upper stability boundary for the at power prole, comparedto the stability boundary of a 20% power skew situation, whichis displayed as a function of Ptop and as a function of Pavg. . . . 93

89

Appendix A

Technical information

Key features of the ESBWR and its predecessors [6].

90

Appendix B

Thermocouple calibration

Figure B.1: Thermocouple signals, including the PT100 signals during coolingdown of the CIRCUS facility before (left) and after calibration (right). The twoimages at the bottom are magnications of the respective upper curves. It canclearly be seen that after calibration the signals are within 0,5 K of each other.

91

Appendix C

Determination of uncertainty

in Npch

The phase change number, Npch is calculated as a function of the power, P andthe mass ow M in equation (4.2):

Npch =P

Mhfg

ρl − ρv

ρv(C.1)

The relative uncertainty in Npch can therefore be determined as a function therelative uncertainties in P and M :

(u(Npch)Npch

)2

=(

1 · u(P )P

)2

+(−1 · u(M)

M

)2

(C.2)

Since it was shown by Weppelman [19] that the relative uncertainty in thedetermination of the power is very small, we van state that:

(u(Npch)Npch

)2

=(−1 · u(M)

M

)2

(C.3)

Or:

u(Npch) = Npchu(M)M

Since the relative uncertainty in the determination of M at low mass ows canbecome as high as 16%, we see similar relative uncertainties in Npch.

92

Appendix D

Power skew trends in the

dimensionless plane

Figure D.1: The upper stability boundary for the at power prole, comparedto the stability boundary of a 20% power skew situation, which is displayed asa function of Ptop and as a function of Pavg.

93

Appendix E

Equipment specications

The next pages contain the information sheets of the ultrabright LED and pho-todiode used in the design of the void sensors.

94

VISHAY TLC.58..

Document Number 83178

Rev. 2, 03-Apr-03

Vishay Semiconductors

www.vishay.com

1

94 8631

Ultrabright LED, ∅ 5 mm Untinted Non-Diffused

\

DescriptionThe TLC.58.. series is a clear, non diffused 5 mm LEDfor high end applications where supreme luminousintensity and a very small emission angle is required.These lamps with clear untinted plastic case utilizethe highly developed ultrabright AlInGaP and GaPtechnologies.The very small viewing angle of these devices providea very high luminous intensity.

Features • Untinted non diffused lens • Utilizing ultrabright AllnGaP and InGaN technol-

ogy • Very high luminous intensity • Very small emission angle • High operating temperature: Tj (chip junction tem-

perature) up to 125 °C for AllnGaP devices • Luminous intensity and color categorized for each

packing unit • ESD-withstand voltage: 2 kV acc. to MIL STD 883

D, Method 3015.7 for AllnGaP, 1 kV for InGaN

ApplicationsInterior and exterior lightingOutdoor LED panels, displaysInstrumentation and front panel indicatorsCentral high mounted stop lights (CHMSL) for motorvehiclesReplaces incandescent lampsTraffic signals and signsLight guide design

Parts Table

Absolute Maximum RatingsTamb = 25 °C, unless otherwise specifiedTLCR5800 , TLCY5800 , TLCTG5800 , TLCB5800

Part Color, Luminous Intensity Technology

TLCR5800 Red, IV > 7500 mcd AllGaP on GaAs

TLCY5800 Yellow, IV > 5750 mcd AllGaP on GaAs

TLCTG5800 True green, IV > 2400 mcd InGaN on SiC

TLCB5800 Blue, IV > 750 mcd InGaN on SiC

Parameter Test condition Part Symbol Value Unit

Reverse voltage VR 5 V

DC forward current Tamb ≤ 85°C TLCR5800 IF 50 mA

Tamb ≤ 85°C TLCR5800 IF 50 mA

Tamb ≤ 60°C TLCTG5800 IF 30 mA

Tamb ≤ 60°C TLCTG5800 IF 30 mA

95

TSL250R, TSL251R, TSL252RLIGHT-TO-VOLTAGE OPTICAL SENSORS

TAOS028F − NOVEMBER 2005

1

The LUMENOLOGY Company

Copyright 2006, TAOS Inc.

www.taosinc.com

Monolithic Silicon IC ContainingPhotodiode, Operational Amplifier, andFeedback Components

Converts Light Intensity to a Voltage

High Irradiance Responsivity, Typically137 mV/(W/cm2) at p = 635 nm (TSL250R)

Compact 3-Lead Clear Plastic Package

Single Voltage Supply Operation

Low Dark (Offset) Voltage....10 mV Max

Low Supply Current......1.1 mA Typical

Wide Supply-Voltage Range.... 2.7 V to 5.5 V

Replacements for TSL250, TSL251, andTSL252

RoHS Compliant (−LF Package Only)

Description

The TSL250R, TSL251R, and TSL252R are light-to-voltage optical sensors, each combining a photodiode anda transimpedance amplifier (feedback resistor = 16 MΩ, 8 MΩ, and 2.8 MΩ respectively) on a single monolithicIC. Output voltage is directly proportional to the light intensity (irradiance) on the photodiode. These deviceshave improved amplifier offset-voltage stability and low power consumption and are supplied in a 3-lead clearplastic sidelooker package with an integral lens. When supplied in the lead (Pb) free package, the device isRoHS compliant.

Functional Block Diagram

VoltageOutput+

−

Available Options

DEVICE TA PACKAGE − LEADS PACKAGE DESIGNATOR ORDERING NUMBER

TSL250R 0°C to 70°C 3-lead Sidelooker S TSL250R

TSL250R 0°C to 70°C 3-lead Sidelooker — Lead (Pb) Free S TSL250R−LF

TSL250R 0°C to 70°C 3-lead Surface-Mount Sidelooker — Lead (Pb) Free SM TSL250RSM−LF

TSL251R 0°C to 70°C 3-lead Sidelooker S TSL251R

TSL251R 0°C to 70°C 3-lead Sidelooker — Lead (Pb) Free S TSL251R−LF

TSL251R 0°C to 70°C 3-lead Surface-Mount Sidelooker — Lead (Pb) Free SM TSL251RSM−LF

TSL252R 0°C to 70°C 3-lead Sidelooker S TSL252R

TSL252R 0°C to 70°C 3-lead Sidelooker — Lead (Pb) Free S TSL252R−LF

TSL252R 0°C to 70°C 3-lead Surface-Mount Sidelooker — Lead (Pb) Free SM TSL252RSM−LF

Texas Advanced Optoelectronic Solutions Inc.1001 Klein Road Suite 300 Plano, TX 75074 (972) 673-0759

PACKAGE SSIDELOOKER(FRONT VIEW)

1GND

2VDD

3OUT

PACKAGE SMSURFACE MOUNT

SIDELOOKER(FRONT VIEW)

1GND

2VDD

3OUT

96